ਗਣਿਤਿਕ ਸਥਿਰਾਂਕ ਅਤੇ ਫੰਕਸ਼ਨ

ਇੱਕ ਗਣਿਤਿਕ ਕੌਂਸਟੈਂਟ ਜਾਂ ਸਥਿਰਾਂਕ ਇੱਕ ਅਜਿਹਾ ਨੰਬਰ (ਸੰਖਿਆ) ਹੁੰਦਾ ਹੈ, ਜਿਸਦਾ ਕੈਲਕੁਲੇਸ਼ਨਾਂ ਲਈ ਇੱਕ ਖਾਸ ਅਰਥ ਹੁੰਦਾ ਹੈ। ਉਦਾਹਰਨ ਦੇ ਤੌਰ 'ਤੇ, ਸਥਿਰਾਂਕ π (ਪਾਈ) ਦਾ ਅਰਥ ਹੈ ਕਿਸੇ ਚੱਕਰ ਦੇ ਘੇਰੇ ਦੀ ਲੰਬਾਈ ਦਾ ਇਸਦੇ ਡਾਇਆਮੀਟਰ (ਅਰਧ-ਵਿਆਸ) ਪ੍ਰਤਿ ਅਨੁਪਾਤ (ਰੇਸ਼ੋ)। ਇਹ ਮੁੱਲ ਹਮੇਸ਼ਾ ਹੀ ਕਿਸੇ ਚੱਕਰ ਲਈ ਇਹੀ ਰਹਿੰਦਾ ਹੈ।

ਸਾਰਣੀਆਂ ਦੀ ਬਣਤਰ

• ਸਥਿਰਾਂਕ ਦਾ ਸੰਖਿਅਕ ਮੁੱਲ ਅਤੇ ਗਣਿਤ-ਸੰਸਾਰ ਨਾਲ ਜਾਂ OEIS ਵਿਕੀ ਨਾਲ ਲਿੰਕ।
• LaTeX: ਫੌਰਮੈਟ ਵਿੱਚ ਫਾਰਮੂਲਾ ਜਾਂ ਸੀਰੀਜ਼।
• ਫਾਰਮੂਲਾ: ਵੌਲਫ੍ਰਾਮ ਅਲਫਾ ਪ੍ਰੋਗਰਾਮ ਅੰਦਰ ਵਰਤੋਂ ਵਾਸਤੇ।
• OEIS: On-Line Encyclopedia of।nteger Sequences।
• ਨਿਰੰਤਰ ਭਿੰਨ: ਰੂਪ [to integer; frac1, frac2, frac3, ...] ਵਿੱਚ ਸਰਲ, ਜੇਕਰ ਪੀਰੀਔਡਿਕ ਹੋਵੇ ਤਾਂ overline।
• ਸਾਲ: ਸਥਿਰਾਂਕ ਦੀ ਖੋਜ, ਜਾਂ ਵਿਦਵਾਨ ਦੀਆਂ ਤਰੀਕਾਂ।
• ਵੈਬ ਫੌਰਮੈਟ: ਵੈਬ ਬਰਾਊਜ਼ਰਾਂ ਲਈ ਢੁਕਵੇਂ ਫੌਰਮੈਟਾਂ ਵਿੱਚ ਮੁੱਲ।
• Nº: ਨੰਬਰ ਕਿਸਮਾਂ।
  • R – ਰੈਸ਼ਨਲ ਸੰਖਿਆ
  • । – ਗੈਰ-ਰੈਸ਼ਨਲ ਸੰਖਿਆ
  • A – ਅਲਜਬ੍ਰਿਕ ਸੰਖਿਆ
  • T – ਟ੍ਰਾਂਸਡੈਂਟਲ ਸੰਖਿਆ
  • C – ਗੈਰ-ਵਾਸਤਵਿਕ ਕੰਪਲੈਕਸ ਨੰਬਰ

ਸਥਿਰਾਂਕਾਂ ਅਤੇ ਫੰਕਸ਼ਨਾਂ ਦੀ ਸਾਰਣੀ

ਨਾਮ, ਮੁੱਲ, OEIS ਅਦਿ ਉੱਤੇ ਕਲਿੱਕ ਕਰਕੇ ਤੁਸੀਂ ਸੂਚੀ ਦੇ ਔਰਡਰ ਨੂੰਚੁਣ ਸਕਦੇ ਹੋ..

ਇਸ ਹਿੱਸੇ/ਲੇਖ ਨੂੰ ਪੰਜਾਬੀ ਵਿੱਚ ਅਨੁਵਾਦ ਕਰਨ ਦੀ ਜਰੂਰਤ ਹੈ ਹੈ। ਤੁਸੀਂ ਇਸਦਾ ਪੰਜਾਬੀ ਵਿੱਚ ਅਨੁਵਾਦ ਕਰਕੇ ਵਿਕੀਪੀਡੀਆ ਦੀ ਮਦਦ ਕਰ ਸਕਦੇ ਹੋ।

Value	Name	Graphics	Symbol	LaTeX	Formula	Nº	OEIS	Continued fraction	Year	Web format
0.74048 04896 93061 04116	Hermite constant Sphere packing 3D Kepler conjecture		${\mu _{_{K}}}$	${\frac {\pi }{3{\sqrt {2}}}}{\color {white}......\color {black}}$ The Flyspeck project, led by Thomas Hales, demonstrated in 2014 that Kepler's conjecture is true.	pi/(3 sqrt(2))		ਫਰਮਾ:OEIS2C	[0;1,2,1,5,1,4,2,2,1,1,2,2,2,6,1,1,1,5,2,1,1,1, ...]	1611	0.74048048969306104116931349834344894
22.45915 77183 61045 47342	pi^e		$\pi ^{e}$	$\pi ^{e}$	pi^e		ਫਰਮਾ:OEIS2C	[22;2,5,1,1,1,1,1,3,2,1,1,3,9,15,25,1,1,5,...]		22.4591577183610454734271522045437350
2.80777 02420 28519 36522	Fransén-Robinson constant		${F}$	$\int _{0}^{\infty }{\frac {1}{\Gamma (x)}}\,dx.=e+\int _{0}^{\infty }{\frac {e^{-x}}{\pi ^{2}+\ln ^{2}x}}\,dx$	N[int[0 to ∞] {1/Gamma(x)}]		ਫਰਮਾ:OEIS2C	[2;1,4,4,1,18,5,1,3,4,1,5,3,6,1,1,1,5,1,1,1...]	1978	2.80777024202851936522150118655777293
1.30568 6729 ≈ by Thomas & Dhar 1.30568 8 ≈ by McMullen	Fractal dimension of the Apollonian packing of circles  ·		$\varepsilon$				ਫਰਮਾ:OEIS2C	[0;3,2,3,16,8,10,3,1,1,2,1,3,1,2,13,1,1,4,1,5,...]	1994 1998	1.305686729 ≈ 1.305688 ≈
0.43828 29367 27032 11162 0.36059 24718 71385 485 i	Infinite Tetration of i		${}^{\infty }{i}$	$\lim _{n\to \infty }{}^{n}i=\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}$	i^i^i^i^i^i^...	C	ਫਰਮਾ:OEIS2C ਫਰਮਾ:OEIS2C	[0;2,3,1,1,4,2,2,1,10,2,1,3,1,8,2,1,2,1, ...] + [0;2,1,3,2,2,3,1,5,5,1,2,1,10,10,6,1,1...] i		0.43828293672703211162697516355126482 + 0.36059247187138548595294052690600 i
0.92883 58271	Sum of the reciprocals of the averages of the twin prime pairs, JJGJJG		$B_{1}$	${\frac {1}{4}}+{\frac {1}{6}}+{\frac {1}{12}}+{\frac {1}{18}}+{\frac {1}{30}}+{\frac {1}{42}}+{\frac {1}{60}}+{\frac {1}{72}}+\cdots$	1/4 + 1/6 + 1/12 + 1/18 + 1/30 + 1/42 + 1/60 + 1/72 + ...		ਫਰਮਾ:OEIS2C	[0; 1, 13, 19, 4, 2, 3, 1, 1]	2014	0.928835827131
0.63092 97535 71457 43709	Fractal dimension of the Cantor set		$d_{f}(k)$	$\lim _{\varepsilon \to 0}{\frac {\log N(\varepsilon )}{\log(1/\varepsilon )}}={\frac {\log 2}{\log 3}}$	log(2)/log(3) N[3^x=2]	T	ਫਰਮਾ:OEIS2C	[0;1,1,1,2,2,3,1,5,2,23,2,2,1,1,55,1,4,3,1,1,...]		0.63092975357145743709952711434276085
0.31830 98861 83790 67153	।nverse of Pi, Ramanujan		${\frac {1}{\pi }}$	${\frac {2{\sqrt {2}}}{9801}}\sum _{n=0}^{\infty }{\frac {(4n)!\,(1103+26390\;n)}{(n!)^{4}\,396^{4n}}}$	2 sqrt(2)/9801 * Sum[n=0 to ∞] {((4n)!/n!^4) *(1103+ 26390n) / 396^(4n)}	T	ਫਰਮਾ:OEIS2C	[0;3,7,15,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,...]		0.31830988618379067153776752674502872
0.28878 80950 86602 42127	Flajolet and Richmond		${Q}$	$\prod _{n=1}^{\infty }\left(1-{\frac {1}{2^{n}}}\right)=\left(1{-}{\frac {1}{2^{1}}}\right)\left(1{-}{\frac {1}{2^{2}}}\right)\left(1{-}{\frac {1}{2^{3}}}\right)...$	prod[n=1 to ∞] {1-1/2^n}		ਫਰਮਾ:OEIS2C	[0;3,2,6,4,1,2,1,9,2,1,2,3,2,3,5,1,2,1,1,6,1,...]	1992	0.28878809508660242127889972192923078
1.53960 07178 39002 03869	Lieb's square ice constant		${W}_{2D}$	$\lim _{n\to \infty }(f(n))^{n^{-2}}=\left({\frac {4}{3}}\right)^{\frac {3}{2}}={\frac {8}{3{\sqrt {3}}}}$	(4/3)^(3/2)	A	ਫਰਮਾ:OEIS2C	[1;1,1,5,1,4,2,1,6,1,6,1,2,4,1,5,1,1,2,...]	1967	1.53960071783900203869106341467188655
0.20787 95763 50761 90854	$i^{i}$		$i^{i}$	$e^{-{\frac {\pi }{2}}}$	e^(-π/2)	T	ਫਰਮਾ:OEIS2C	[0;4,1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,...]	1746	0.20787957635076190854695561983497877
4.53236 01418 27193 80962	Van der Pauw constant		${\alpha }$	${\frac {\pi }{\ln(2)}}={\frac {\sum \limits _{n=0}^{\infty }{\frac {4(-1)^{n}}{2n+1}}}{\sum \limits _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}}}={\frac {{\frac {4}{1}}-{\frac {4}{3}}+{\frac {4}{5}}-{\frac {4}{7}}+{\frac {4}{9}}-\cdots }{{\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\frac {1}{5}}-\cdots }}$	π/ln(2)		ਫਰਮਾ:OEIS2C	[4;1,1,7,4,2,3,3,1,4,1,1,4,7,2,3,3,12,2,1,...]		4.53236014182719380962768294571666681
0.76159 41559 55764 88811	Hyperbolic tangent of 1		${th}\,1$	$-i\tan(i)={\frac {e-{\frac {1}{e}}}{e+{\frac {1}{e}}}}={\frac {e^{2}-1}{e^{2}+1}}$	(e-1/e)/(e+1/e)	T	ਫਰਮਾ:OEIS2C	[0;1,3,5,7,9,11,13,15,17,19,21,23,25,27,...] = [0;2p+1], p∈ℕ		0.76159415595576488811945828260479359
0.59017 02995 08048 11302	Chebyshev constant ·		${\lambda _{Ch}}$	${\frac {\Gamma ({\tfrac {1}{4}})^{2}}{4\pi ^{3/2}}}={\frac {4({\tfrac {1}{4}}!)^{2}}{\pi ^{3/2}}}$	(Gamma(1/4)^2) /(4 pi^(3/2))		ਫਰਮਾ:OEIS2C	[0;1,1,2,3,1,2,41,1,6,5,124,5,2,2,1,1,6,1,2,...]		0.59017029950804811302266897027924429
0.07077 60393 11528 80353 -0.68400 03894 37932 129 i	MKB constant  ·  ·		$M_{I}$	$\lim _{n\rightarrow \infty }\int _{1}^{2n}(-1)^{x}~{\sqrt[{x}]{x}}~dx=\int _{1}^{2n}e^{i\pi x}~x^{1/x}~dx$	lim_(2n->∞) int[1 to 2n] {exp(i*Pi*x)*x^(1/x) dx}	C	ਫਰਮਾ:OEIS2C ਫਰਮਾ:OEIS2C	[0;14,7,1,2,1,23,2,1,8,16,1,1,3,1,26,1,6,1,1, ...] - [0;1,2,6,13,41,112,1,25,1,1,1,1,3,13,2,1, ...] i	2009	0.07077603931152880353952802183028200 -0.68400038943793212918274445999266 i
1.25992 10498 94873 16476	Cube root of 2 Delian Constant		${\sqrt[{3}]{2}}$	${\sqrt[{3}]{2}}$	2^(1/3)	A	ਫਰਮਾ:OEIS2C	[1;3,1,5,1,1,4,1,1,8,1,14,1,10,2,1,4,12,2,3,...]		1.25992104989487316476721060727822835
1.09317 04591 95490 89396	Smarandache Constant 1ª		${S_{1}}$	$\sum _{n=2}^{\infty }{\frac {1}{\mu (n)!}}{\color {white}....\color {black}}$ where μ(n) is the Kempner function			ਫਰਮਾ:OEIS2C	[1;10,1,2,1,2,1,13,3,1,6,1,2,11,4,6,2,15,1,1,...]		1.09317045919549089396820137014520832
0.62481 05338 43826 58687 + 1.30024 25902 20120 419 i	Generalized continued fraction of i		${{F}_{CG}}_{(i)}$	$\textstyle i{+}{\frac {i}{i+{\frac {i}{i+{\frac {i}{i+{\frac {i}{i+{\frac {i}{i+{\frac {i}{i+i{/...}}}}}}}}}}}}}={\sqrt {\frac {{\sqrt {17}}-1}{8}}}+i\left({\tfrac {1}{2}}{+}{\sqrt {\frac {2}{{\sqrt {17}}-1}}}\right)$	i+i/(i+i/(i+i/(i+i/(i+i/( i+i/(i+i/(i+i/(i+i/(i+i/( i+i/(i+i/(i+i/(i+i/(i+i/( i+i/(i+i/(i+i/(i+i/(i+i/( ...)))))))))))))))))))))	C A	ਫਰਮਾ:OEIS2C ਫਰਮਾ:OEIS2C	[i;1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,..] = [0;1,i]		0.62481053384382658687960444744285144 + 1.30024259022012041915890982074952 i
3.05940 74053 42576 14453	Double factorial constant		${C_{_{n!!}}}$	$\sum _{n=0}^{\infty }{\frac {1}{n!!}}={\sqrt {e}}\left[{\frac {1}{\sqrt {2}}}+\gamma ({\tfrac {1}{2}},{\tfrac {1}{2}})\right]$	Sum[n=0 to ∞]{1/n!!}		ਫਰਮਾ:OEIS2C	[3;16,1,4,1,66,10,1,1,1,1,2,5,1,2,1,1,1,1,1,2,...]		3.05940740534257614453947549923327861
5.97798 68121 78349 12266	Madelung Constant 2		${H}_{2}(2)$	$\pi \ln(3){\sqrt {3}}$	Pi Log[3]Sqrt[3]		ਫਰਮਾ:OEIS2C	[5;1,44,2,2,1,15,1,1,12,1,65,11,1,3,1,1,...]		5.97798681217834912266905331933922774
0.91893 85332 04672 74178	Raabe's formula		${\zeta '(0)}$	$\int \limits _{a}^{a+1}\log \Gamma (t)\,\mathrm {d} t={\tfrac {1}{2}}\log 2\pi +a\log a-a,\quad a\geq 0$	integral_a^(a+1) {log(Gamma(x))+a-a log(a)} dx		ਫਰਮਾ:OEIS2C	[0;1,11,2,1,36,1,1,3,3,5,3,1,18,2,1,1,2,2,1,1,...]		0.91893853320467274178032973640561763
2.20741 60991 62477 96230	Lower limit in the moving sofa problem		${S_{_{H}}}$	${\frac {\pi }{2}}+{\frac {2}{\pi }}$	pi/2 + 2/pi	T	ਫਰਮਾ:OEIS2C	[2;4,1,4,1,1,2,5,1,11,1,1,5,1,6,1,3,1,1,1,1,7,...]	1967	2.20741609916247796230685674512980889
1.17628 08182 59917 50654	Salem number, Lehmer's conjecture		${\sigma _{_{10}}}$	$x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1$	x^10+x^9-x^7-x^6 -x^5-x^4-x^3+x+1	A	ਫਰਮਾ:OEIS2C	[1;5,1,2,17,1,7,2,1,1,2,4,7,2,2,1,1,15,1,1, ...	1983?	1.17628081825991750654407033847403505
0.37395 58136 19202 28805	Artin constant		${C}_{Artin}$	$\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}(p_{n}-1)}}\right)\quad p_{n}\scriptstyle {\text{ = prime}}$	Prod[n=1 to ∞] {1-1/(prime(n) (prime(n)-1))}		ਫਰਮਾ:OEIS2C	[0;2,1,2,14,1,1,2,3,5,1,3,1,5,1,1,2,3,5,46,...]	1999	0.37395581361920228805472805434641641
0.42215 77331 15826 62702	Volume of Reuleaux tetrahedron		${V_{_{R}}}$	${\frac {s^{3}}{12}}(3{\sqrt {2}}-49\,\pi +162\,\arctan {\sqrt {2}})$	(3*Sqrt[2] - 49*Pi + 162*ArcTan[Sqrt[2]])/12		ਫਰਮਾ:OEIS2C	[0;2,2,1,2,2,7,4,4,287,1,6,1,2,1,8,5,1,1,1,1, ...]		0.42215773311582662702336591662385075
2.82641 99970 67591 57554	Murata Constant		${C_{m}}$	$\prod _{n=1}^{\infty }{\underset {p_{n}:\,{prime}}{{\Big (}1+{\frac {1}{(p_{n}-1)^{2}}}{\Big )}}}$	Prod[n=1 to ∞] {1+1/(prime(n) -1)^2}		ਫਰਮਾ:OEIS2C	[2;1,4,1,3,5,2,2,2,4,3,2,1,3,2,1,1,1,8,2,2,28,...]		2.82641999706759157554639174723695374
1.09864 19643 94156 48573	Paris Constant		$C_{Pa}$	$\prod _{n=2}^{\infty }{\frac {2\varphi }{\varphi +\varphi _{n}}}\;,\;\varphi {=}{Fi}$ con $\varphi _{n}{=}{\sqrt {1{+}\varphi _{n{-}1}}}$ y $\varphi _{1}{=}1$			ਫਰਮਾ:OEIS2C	[1;10,7,3,1,3,1,5,1,4,2,7,1,2,3,22,1,2,5,2,1,...]		1.09864196439415648573466891734359621
2.39996 32297 28653 32223 Radians	Golden angle		${b}$	$(4-2\,\Phi )\,\pi =(3-{\sqrt {5}})\,\pi$ = 137.5077640500378546 ...°	(4-2*Phi)*Pi	T	ਫਰਮਾ:OEIS2C	[2;2,1,1,1087,4,4,120,2,1,1,2,1,1,7,7,2,11,...]	1907	2.39996322972865332223155550663361385
1.64218 84352 22121 13687	Lebesgue constant L2		${L2}$	${\frac {1}{5}}+{\frac {\sqrt {25-2{\sqrt {5}}}}{\pi }}={\frac {1}{\pi }}\int _{0}^{\pi }{\frac {\left|\sin({\frac {5t}{2}})\right|}{\sin({\frac {t}{2}})}}\,dt$	1/5 + sqrt(25 - 2*sqrt(5))/Pi	T	ਫਰਮਾ:OEIS2C	[1;1,1,1,3,1,6,1,5,2,2,3,1,2,7,1,3,5,2,2,1,1,...]	1910	1.64218843522212113687362798892294034
1.26408 47353 05301 11307	Vardi constant		${V_{c}}$	${\frac {\sqrt {3}}{\sqrt {2}}}\prod _{n\geq 1}\left(1+{1 \over (2e_{n}-1)^{2}}\right)^{\!1/2^{n+1}}$			ਫਰਮਾ:OEIS2C	[1;3,1,3,1,2,5,54,7,1,2,1,2,3,15,1,2,1,1,2,1,...]	1991	1.26408473530530111307959958416466949
1.5065918849 ± 0.0000000028	Area of the Mandelbrot fractal		$\gamma$	This is conjectured to be: ${\sqrt {6\pi -1}}-e=1.506591651\cdots$			ਫਰਮਾ:OEIS2C	[1;1,1,37,2,2,1,10,1,1,2,2,4,1,1,1,1,5,4,...]	1912	1.50659177 +/- 0.00000008
1.61111 49258 08376 736 111···111 27224 36828 183213 ones	Exponential factorial constant		${S_{Ef}}$	$\sum _{n=1}^{\infty }{\frac {1}{n^{(n{-}1)^{\cdot ^{\cdot ^{\cdot ^{2^{1}}}}}}}}=1{+}{\frac {1}{2^{1}}}{+}{\frac {1}{3^{2^{1}}}}+{\frac {1}{4^{3^{2^{1}}}}}+{\frac {1}{5^{4^{3^{2^{1}}}}}}{+}\cdots$		T	ਫਰਮਾ:OEIS2C	[1; 1, 1, 1, 1, 2, 1, 808, 2, 1, 2, 1, 14,...]		1.61111492580837673611111111111111111
1.11786 41511 89944 97314	Goh-Schmutz constant		$C_{GS}$	$\int _{0}^{\infty }{\frac {\log(s+1)}{e^{s}-1}}\ ds=\!-\!\sum _{n=1}^{\infty }{\frac {e^{n}}{n}}Ei(-n)$ Ei: Exponential।ntegral	Integrate{ log(s+1) /(E^s-1)}		ਫਰਮਾ:OEIS2C	[1;8,2,15,2,7,2,1,1,1,1,2,3,5,3,5,1,1,4,13,1,...]		1.11786415118994497314040996202656544
0.31813 15052 04764 13531 ±1.33723 57014 30689 40 i	Fixed points Super-Logarithm · Tetration		${-W(-1)}$	$\lim _{n\rightarrow \infty }$$f(x)=\underbrace {\log(\log(\log(\log(\cdots \log(\log(x))))))\,\!} \atop {\log _{s}{\text{ n times}}}$ For an initial value of x different to ${\textstyle 0,1,e,e^{e},e^{e^{e}}}$, etc.	-W(-1) where W=ProductLog Lambert W function	C	ਫਰਮਾ:OEIS2C ਫਰਮਾ:OEIS2C	[-i;1 +2i,1+i,6-i,1+2i,-7+3i,2i,2,1-2i,-1+i,-, ...]		0.31813150520476413531265425158766451 -1.33723570143068940890116214319371 i
0.28016 94990 23869 13303	Bernstein's constant		${\beta }$	$\approx {\frac {1}{2{\sqrt {\pi }}}}$	1/(2 sqrt(pi))	T	ਫਰਮਾ:OEIS2C	[0;3,1,1,3,9,6,3,1,3,14,34,2,1,1,60,2,2,1,1,...]	1913	0.28016949902386913303643649123067200
0.66016 18158 46869 57392	Twin Primes Constant		${C}_{2}$	$\prod _{p=3}^{\infty }{\frac {p(p-2)}{(p-1)^{2}}}$	prod[p=3 to ∞] {p(p-2)/(p-1)^2		ਫਰਮਾ:OEIS2C	[0;1,1,1,16,2,2,2,2,1,18,2,2,11,1,1,2,4,1,...]	1922	0.66016181584686957392781211001455577
1.22674 20107 20353 24441	Fibonacci Factorial constant		$F$	$\prod _{n=1}^{\infty }\left(1-\left(-{\frac {1}{{\varphi }^{2}}}\right)^{n}\right)=\prod _{n=1}^{\infty }\left(1-\left({\frac {{\sqrt {5}}-3}{2}}\right)^{n}\right)$	prod[n=1 to ∞] {1-((sqrt(5) -3)/2)^n}		ਫਰਮਾ:OEIS2C	[1;4,2,2,3,2,15,9,1,2,1,2,15,7,6,21,3,5,1,23,...]		1.22674201072035324441763023045536165
0.11494 20448 53296 20070	Kepler–Bouwkamp constant		${\rho }$	$\prod _{n=3}^{\infty }\cos \left({\frac {\pi }{n}}\right)=\cos \left({\frac {\pi }{3}}\right)\cos \left({\frac {\pi }{4}}\right)\cos \left({\frac {\pi }{5}}\right)...$	prod[n=3 to ∞] {cos(pi/n)}		ਫਰਮਾ:OEIS2C	[0;8,1,2,2,1,272,2,1,41,6,1,3,1,1,26,4,1,1,...]		0.11494204485329620070104015746959874
1.78723 16501 82965 93301	Komornik–Loreti constant		${q}$	$1=\!\sum _{n=1}^{\infty }{\frac {t_{k}}{q^{k}}}\qquad \scriptstyle {\text{Raiz real de}}\displaystyle \prod _{n=0}^{\infty }\!\left(\!1{-}{\frac {1}{q^{2^{n}}}}\!\right)\!{+}{\frac {q{-}2}{q{-}1}}=0$ tk = Thue–Morse sequence	FindRoot[(prod[n=0 to ∞] {1-1/(x^2^n)}+(x-2) /(x-1))= 0, {x, 1.7}, WorkingPrecision->30]	T	ਫਰਮਾ:OEIS2C	[1;1,3,1,2,3,188,1,12,1,1,22,33,1,10,1,1,7,...]	1998	1.78723165018296593301327489033700839
3.30277 56377 31994 64655	Bronze ratio		${\sigma }_{\,Rr}$	${\frac {3+{\sqrt {13}}}{2}}=1+{\sqrt {3+{\sqrt {3+{\sqrt {3+{\sqrt {3+\cdots }}}}}}}}$	(3+sqrt 13)/2	A	ਫਰਮਾ:OEIS2C	[3;3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,...] = [3;3,...]		3.30277563773199464655961063373524797
0.82699 33431 32688 07426	Disk Covering		${C_{5}}$	${\frac {1}{\sum \limits _{n=0}^{\infty }{\frac {1}{\binom {3n+2}{2}}}}}={\frac {3{\sqrt {3}}}{2\pi }}$	3 Sqrt[3]/(2 Pi)	T	ਫਰਮਾ:OEIS2C	[0;1,4,1,3,1,1,4,1,2,2,1,1,7,1,4,4,2,1,1,1,1,...]	1939 1949	0.82699334313268807426698974746945416
2.66514 41426 90225 18865	Gelfond–Schneider constant		$G_{\,GS}$	$2^{\sqrt {2}}$	2^sqrt{2}	T	ਫਰਮਾ:OEIS2C	[2;1,1,1,72,3,4,1,3,2,1,1,1,14,1,2,1,1,3,1,...]	1934	2.66514414269022518865029724987313985
3.27582 29187 21811 15978	Khinchin-Lévy constant		$\gamma$	$e^{\pi ^{2}/(12\ln 2)}$	e^(\pi^2/(12 ln(2))		ਫਰਮਾ:OEIS2C	[3;3,1,1,1,2,29,1,130,1,12,3,8,2,4,1,3,55,...]	1936	3.27582291872181115978768188245384386
0.52382 25713 89864 40645	Chi Function Hyperbolic cosine integral		${\operatorname {Chi()} }$	$\gamma +\int _{0}^{x}{\frac {\cosh t-1}{t}}\,dt$ $\scriptstyle \gamma \,{\text{= Euler–Mascheroni constant= 0.5772156649...}}$	Chi(x)		ਫਰਮਾ:OEIS2C	[0;1,1,9,1,172,1,7,1,11,1,1,2,1,8,1,1,1,1,1,...]		0.52382257138986440645095829438325566
1.13198 82487 943	Viswanath constant		${C}_{Vi}$	$\lim _{n\to \infty }|a_{n}|^{\frac {1}{n}}$ where an = Fibonacci sequence	lim_(n->∞) |a_n|^(1/n)	T ?	ਫਰਮਾ:OEIS2C	[1;7,1,1,2,1,3,2,1,2,1,8,1,5,1,1,1,9,1,...]	1997	1.1319882487943 ...
1.23370 05501 36169 82735	Favard constant		${\tfrac {3}{4}}\zeta (2)$	${\frac {\pi ^{2}}{8}}=\sum _{n=0}^{\infty }{\frac {1}{(2n-1)^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}+\cdots$	sum[n=1 to ∞] {1/((2n-1)^2)}	T	ਫਰਮਾ:OEIS2C	[1;4,3,1,1,2,2,5,1,1,1,1,2,1,2,1,10,4,3,1,1,...]	1902 a 1965	1.23370055013616982735431137498451889
2.50662 82746 31000 50241	Square root of 2 pi		${\sqrt {2\pi }}$	${\sqrt {2\pi }}=\lim _{n\to \infty }{\frac {n!\;e^{n}}{n^{n}{\sqrt {n}}}}{\color {white}....\color {black}}$ Stirling's approximation	sqrt (2 pi)	T	ਫਰਮਾ:OEIS2C	[2;1,1,37,4,1,1,1,1,9,1,1,2,8,6,1,2,2,1,3,...]	1692 a 1770	2.50662827463100050241576528481104525
4.13273 13541 22492 93846	Square root of Tau·e		${\sqrt {\tau e}}$	${\sqrt {2\pi e}}$	sqrt(2 pi e)		ਫਰਮਾ:OEIS2C	[4;7,1,1,6,1,5,1,1,1,8,3,1,2,2,15,2,1,1,2,4,...]		4.13273135412249293846939188429985264
0.97027 01143 92033 92574	Lochs constant		${{\text{£}}_{_{Lo}}}$	${\frac {6\ln 2\ln 10}{\pi ^{2}}}$	6*ln(2)*ln(10)/Pi^2		ਫਰਮਾ:OEIS2C	[0;1,32,1,1,1,2,1,46,7,2,7,10,8,1,71,1,37,1,1,...]	1964	0.97027011439203392574025601921001083
0.98770 03907 36053 46013	Area bounded by the eccentric rotation of Reuleaux triangle		${\mathcal {T}}_{R}$	$a^{2}\cdot \left(2{\sqrt {3}}+{\frac {\pi }{6}}-3\right)$ where a= side length of the square	2 sqrt(3)+pi/6-3	T	ਫਰਮਾ:OEIS2C	[0;1,80,3,3,2,1,1,1,4,2,2,1,1,1,8,1,2,10,1,2,...]	1914	0.98770039073605346013199991355832854
0.70444 22009 99165 59273	Carefree constant 2		${\mathcal {C}}_{2}$	${\underset {p_{n}:\,{prime}}{\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}(p_{n}+1)}}\right)}}$	N[prod[n=1 to ∞] {1 - 1/(prime(n)* (prime(n)+1))}]		ਫਰਮਾ:OEIS2C	[0;1,2,2,1,1,1,1,4,2,1,1,3,703,2,1,1,1,3,5,1,...]		0.70444220099916559273660335032663721
1.84775 90650 22573 51225	Connective constant		${\mu }$	${\sqrt {2+{\sqrt {2}}}}\;=\lim _{n\rightarrow \infty }c_{n}^{1/n}$ as a root of the polynomial $:\;x^{4}-4x^{2}+2=0$	sqrt(2+sqrt(2))	A	ਫਰਮਾ:OEIS2C	[1;1,5,1,1,3,6,1,3,3,10,10,1,1,1,5,2,3,1,1,3,...]		1.84775906502257351225636637879357657
0.30366 30028 98732 65859	Gauss-Kuzmin-Wirsing constant		${\lambda }_{2}$	$\lim _{n\to \infty }{\frac {F_{n}(x)-\ln(1-x)}{(-\lambda )^{n}}}=\Psi (x),$ where $\Psi (x)$ is an analytic function with $\Psi (0)\!=\!\Psi (1)\!=\!0$.			ਫਰਮਾ:OEIS2C	[0;3,3,2,2,3,13,1,174,1,1,1,2,2,2,1,1,1,2,2,1,...]	1973	0.30366300289873265859744812190155623
1.57079 63267 94896 61923	Favard constant K1 Wallis product		${\frac {\pi }{2}}$	$\prod _{n=1}^{\infty }\left({\frac {4n^{2}}{4n^{2}-1}}\right)={\frac {2}{1}}\cdot {\frac {2}{3}}\cdot {\frac {4}{3}}\cdot {\frac {4}{5}}\cdot {\frac {6}{5}}\cdot {\frac {6}{7}}\cdot {\frac {8}{7}}\cdot {\frac {8}{9}}\cdots$	Prod[n=1 to ∞] {(4n^2)/(4n^2-1)}	T	ਫਰਮਾ:OEIS2C	[1;1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,1,5,1...]	1655	1.57079632679489661923132169163975144
1.60669 51524 15291 76378	Erdős–Borwein constant		${E}_{\,B}$	$\sum _{m=1}^{\infty }\sum _{n=1}^{\infty }{\frac {1}{2^{mn}}}=\sum _{n=1}^{\infty }{\frac {1}{2^{n}-1}}={\frac {1}{1}}\!+\!{\frac {1}{3}}\!+\!{\frac {1}{7}}\!+\!{\frac {1}{15}}\!+\!...$	sum[n=1 to ∞] {1/(2^n-1)}	I	ਫਰਮਾ:OEIS2C	[1;1,1,1,1,5,2,1,2,29,4,1,2,2,2,2,6,1,7,1,...]	1949	1.60669515241529176378330152319092458
1.61803 39887 49894 84820	Phi, Golden ratio		${\varphi }$	${\frac {1+{\sqrt {5}}}{2}}={\sqrt {1+{\sqrt {1+{\sqrt {1+{\sqrt {1+\cdots }}}}}}}}$	(1+5^(1/2))/2	A	ਫਰਮਾ:OEIS2C	[0;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...] = [0;1,...]	-300 ~	1.61803398874989484820458683436563811
1.64493 40668 48226 43647	Riemann Function Zeta(2)		${\zeta }(\,2)$	${\frac {\pi ^{2}}{6}}=\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{4^{2}}}+\cdots$	Sum[n=1 to ∞] {1/n^2}	T	ਫਰਮਾ:OEIS2C	[1;1,1,1,4,2,4,7,1,4,2,3,4,10 1,2,1,1,1,15,...]	1826 to 1866	1.64493406684822643647241516664602519
1.73205 08075 68877 29352	Theodorus constant		${\sqrt {3}}$	${\sqrt[{3}]{3\,{\sqrt[{3}]{3\,{\sqrt[{3}]{3\,{\sqrt[{3}]{3\,{\sqrt[{3}]{3\,\cdots }}}}}}}}}}$	(3(3(3(3(3(3(3) ^1/3)^1/3)^1/3) ^1/3)^1/3)^1/3) ^1/3 ...	A	ਫਰਮਾ:OEIS2C	[1;1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,...] = [1;1,2,...]	-465 to -398	1.73205080756887729352744634150587237
1.75793 27566 18004 53270	Kasner number		${R}$	${\sqrt {1+{\sqrt {2+{\sqrt {3+{\sqrt {4+\cdots }}}}}}}}$	Fold[Sqrt[#1+#2] &,0,Reverse [Range[20]]]		ਫਰਮਾ:OEIS2C	[1;1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2,...]	1878 a 1955	1.75793275661800453270881963821813852
2.29558 71493 92638 07403	Universal parabolic constant		${P}_{\,2}$	$\ln(1+{\sqrt {2}})+{\sqrt {2}}\;=\;\operatorname {arcsinh} (1)+{\sqrt {2}}$	ln(1+sqrt 2)+sqrt 2	T	ਫਰਮਾ:OEIS2C	[2;3,2,1,1,1,1,3,3,1,1,4,2,3,2,7,1,6,1,8,7,2,1,...]		2.29558714939263807403429804918949038
1.78657 64593 65922 46345	Silverman constant		${{\mathcal {S}}_{_{m}}}$	$\sum _{n=1}^{\infty }{\frac {1}{\phi (n)\sigma _{1}(n)}}={\underset {p_{n}:\,{prime}}{\prod _{n=1}^{\infty }\left(1+\sum _{k=1}^{\infty }{\frac {1}{p_{n}^{2k}-p_{n}^{k-1}}}\right)}}$ ø() = Euler's totient function, σ1() = Divisor function.	Sum[n=1 to ∞] {1/[EulerPhi(n) DivisorSigma(1,n)]}		ਫਰਮਾ:OEIS2C	[1;1,3,1,2,5,1,65,11,2,1,2,13,1,4,1,1,1,2,5,4,...]		1.78657645936592246345859047554131575
2.59807 62113 53315 94029	Area of the regular hexagon with side equal to 1		${\mathcal {A}}_{6}$	${\frac {3{\sqrt {3}}}{2}}$	3 sqrt(3)/2	A	ਫਰਮਾ:OEIS2C	[2;1,1,2,20,2,1,1,4,1,1,2,20,2,1,1,4,1,1,2,20,...] [2;1,1,2,20,2,1,1,4]		2.59807621135331594029116951225880855
0.66131 70494 69622 33528	Feller-Tornier constant		${{\mathcal {C}}_{_{FT}}}$	${\underset {p_{n}:\,{prime}}{{\frac {1}{2}}\prod _{n=1}^{\infty }\left(1-{\frac {2}{p_{n}^{2}}}\right){+}{\frac {1}{2}}}}={\frac {3}{\pi ^{2}}}\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}^{2}-1}}\right){+}{\frac {1}{2}}$	[prod[n=1 to ∞] {1-2/prime(n)^2}] /2 + 1/2	T ?	ਫਰਮਾ:OEIS2C	[0;1,1,1,20,9,1,2,5,1,2,3,2,3,38,8,1,16,2,2,...]	1932	0.66131704946962233528976584627411853
1.46099 84862 06318 35815	Baxter's Four-coloring constant	Mapamundi Four-Coloring	${\mathcal {C}}^{2}$	$\prod _{n=1}^{\infty }{\frac {(3n-1)^{2}}{(3n-2)(3n)}}={\frac {3}{4\pi ^{2}}}\,\Gamma \left({\frac {1}{3}}\right)^{3}$ Γ() = Gamma function	3×Gamma(1/3) ^3/(4 pi^2)		ਫਰਮਾ:OEIS2C	[1;2,5,1,10,8,1,12,3,1,5,3,5,8,2,1,23,1,2,161,...]	1970	1.46099848620631835815887311784605969
1.92756 19754 82925 30426	Tetranacci constant		${\mathcal {T}}$	Positive root of $:\;\;x^{4}-x^{3}-x^{2}-x-1=0$	Root[x+x^-4-2=0]	A	ਫਰਮਾ:OEIS2C	[1;1,12,1,4,7,1,21,1,2,1,4,6,1,10,1,2,2,1,7,1,...]		1.92756197548292530426190586173662216
1.00743 47568 84279 37609	DeVicci's tesseract constant		${f_{(3,4)}}$	The largest cube that can pass through in an 4D hypercube. Positive root of $:\;\;4x^{4}{-}28x^{3}{-}7x^{2}{+}16x{+}16=0$	Root[4*x^8-28*x^6 -7*x^4+16*x^2+16 =0]	A	ਫਰਮਾ:OEIS2C	[1;134,1,1,73,3,1,5,2,1,6,3,11,4,1,5,5,1,1,48,...]		1.00743475688427937609825359523109914
1.70521 11401 05367 76428	Niven's constant		${C}$	$1+\sum _{n=2}^{\infty }\left(1-{\frac {1}{\zeta (n)}}\right)$	1+ Sum[n=2 to ∞] {1-(1/Zeta(n))}		ਫਰਮਾ:OEIS2C	[1;1,2,2,1,1,4,1,1,3,4,4,8,4,1,1,2,1,1,11,1,...]	1969	1.70521114010536776428855145343450816
0.60459 97880 78072 61686	Relationship among the area of an equilateral triangle and the inscribed circle.		${\frac {\pi }{3{\sqrt {3}}}}$	$\sum _{n=1}^{\infty }{\frac {1}{n{2n \choose n}}}=1-{\frac {1}{2}}+{\frac {1}{4}}-{\frac {1}{5}}+{\frac {1}{7}}-{\frac {1}{8}}+\cdots$ Dirichlet series	Sum[1/(n Binomial[2 n, n]) , {n, 1, ∞}]	T	ਫਰਮਾ:OEIS2C	[0;1,1,1,1,8,10,2,2,3,3,1,9,2,5,4,1,27,27,6,6,...]		0.60459978807807261686469275254738524
1.15470 05383 79251 52901	Hermite constant		$\gamma _{_{2}}$	${\frac {2}{\sqrt {3}}}={\frac {1}{\cos \,({\frac {\pi }{6}})}}$	2/sqrt(3)	A	1+ ਫਰਮਾ:OEIS2C	[1;6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,...] [1;6,2]		1.15470053837925152901829756100391491
0.41245 40336 40107 59778	Prouhet–Thue–Morse constant		$\tau$	$\sum _{n=0}^{\infty }{\frac {t_{n}}{2^{n+1}}}$ where ${t_{n}}$ is the Thue–Morse sequence and Where $\tau (x)=\sum _{n=0}^{\infty }(-1)^{t_{n}}\,x^{n}=\prod _{n=0}^{\infty }(1-x^{2^{n}})$		T	ਫਰਮਾ:OEIS2C	[0;2,2,2,1,4,3,5,2,1,4,2,1,5,44,1,4,1,2,4,1,1,...]		0.41245403364010759778336136825845528
0.58057 75582 04892 40229	Pell constant		${{\mathcal {P}}_{_{Pell}}}$	$1-\prod _{n=0}^{\infty }\left(1-{\frac {1}{2^{2n+1}}}\right)$	N[1-prod[n=0 to ∞] {1-1/(2^(2n+1)}]	T ?	ਫਰਮਾ:OEIS2C	[0;1,1,2,1,1,1,1,14,1,3,1,1,6,9,18,7,1,27,1,1,...]		0.58057755820489240229004389229702574
0.66274 34193 49181 58097	Laplace limit		${\lambda }$	${\frac {x\;e^{\sqrt {x^{2}+1}}}{{\sqrt {x^{2}+1}}+1}}=1$	(x e^sqrt(x^2+1)) /(sqrt(x^2+1)+1) = 1		ਫਰਮਾ:OEIS2C	[0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,1,1,2,1601,...]	1782 ~	0.66274341934918158097474209710925290
0.17150 04931 41536 06586	Hall-Montgomery Constant		${{\delta }_{_{0}}}$	$1+{\frac {\pi ^{2}}{6}}+2\;\mathrm {Li} _{2}\left(-{\sqrt {e}}\;\right)\quad \mathrm {Li} _{2}\,\scriptstyle {\text{= Dilogarithm integral}}$	1 + Pi^2/6 + 2*PolyLog[2, -Sqrt[E]]		ਫਰਮਾ:OEIS2C	[0;5,1,4,1,10,1,1,11,18,1,2,19,14,1,51,1,2,1,...]		0.17150049314153606586043997155521210
1.55138 75245 48320 39226	Calabi triangle constant		${C_{_{CR}}}$	${1 \over 3}+{(-23+3i{\sqrt {237}})^{\tfrac {1}{3}} \over 3\cdot 2^{\tfrac {2}{3}}}+{11 \over 3(2(-23+3i{\sqrt {237}}))^{\tfrac {1}{3}}}$	FindRoot[ 2x^3-2x^2-3x+2 ==0, {x, 1.5}, WorkingPrecision->40]	A	ਫਰਮਾ:OEIS2C	[1;1,1,4,2,1,2,1,5,2,1,3,1,1,390,1,1,2,11,6,2,...]	1946 ~	1.55138752454832039226195251026462381
1.22541 67024 65177 64512	Gamma(3/4)		$\Gamma ({\tfrac {3}{4}})$	$\left(-1+{\frac {3}{4}}\right)!=\left(-{\frac {1}{4}}\right)!$	(-1+3/4)!		ਫਰਮਾ:OEIS2C	[1;4,2,3,2,2,1,1,1,2,1,4,7,1,171,3,2,3,1,1,8,3,...]		1.22541670246517764512909830336289053
1.20205 69031 59594 28539	Apéry's constant		$\zeta (3)$	$\sum _{n=1}^{\infty }{\frac {1}{n^{3}}}={\frac {1}{1^{3}}}+{\frac {1}{2^{3}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{3}}}+{\frac {1}{5^{3}}}+\cdots =$ ${\frac {1}{2}}\sum _{n=1}^{\infty }{\frac {H_{n}}{n^{2}}}={\frac {1}{2}}\sum _{i=1}^{\infty }\sum _{j=1}^{\infty }{\frac {1}{ij(i{+}j)}}=\!\!\int \limits _{0}^{1}\!\!\int \limits _{0}^{1}\!\!\int \limits _{0}^{1}{\frac {\mathrm {d} x\mathrm {d} y\mathrm {d} z}{1-xyz}}$	Sum[n=1 to ∞] {1/n^3}	I	ਫਰਮਾ:OEIS2C	[1;4,1,18,1,1,1,4,1,9,9,2,1,1,1,2,7,1,1,7,11,...]	1979	1.20205690315959428539973816151144999
0.91596 55941 77219 01505	Catalan's constant		${C}$	$\int _{0}^{1}\!\!\int _{0}^{1}\!\!{\frac {1}{1{+}x^{2}y^{2}}}\,dx\,dy=\!\sum _{n=0}^{\infty }\!{\frac {(-1)^{n}}{(2n{+}1)^{2}}}\!=\!{\frac {1}{1^{2}}}{-}{\frac {1}{3^{2}}}{+}{\cdots }$	Sum[n=0 to ∞] {(-1)^n/(2n+1)^2}	T	ਫਰਮਾ:OEIS2C	[0;1,10,1,8,1,88,4,1,1,7,22,1,2,3,26,1,11,...]	1864	0.91596559417721901505460351493238411
0.78539 81633 97448 30961	Beta(1)		${\beta }(1)$	${\frac {\pi }{4}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{2n+1}}={\frac {1}{1}}-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}-\cdots$	Sum[n=0 to ∞] {(-1)^n/(2n+1)}	T	ਫਰਮਾ:OEIS2C	[0; 1,3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,1,1,10,...]	1805 to 1859	0.78539816339744830961566084581987572
0.00131 76411 54853 17810	Heath-Brown–Moroz constant		${C_{_{HBM}}}$	${\underset {p_{n}:\,{prime}}{\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}}}\right)^{7}\left(1+{\frac {7p_{n}+1}{p_{n}^{2}}}\right)}}$	N[prod[n=1 to ∞] {((1-1/prime(n))^7) *(1+(7*prime(n)+1) /(prime(n)^2))}]	T ?	ਫਰਮਾ:OEIS2C	[0;758,1,13,1,2,3,56,8,1,1,1,1,1,143,1,1,1,2,...]		0.00131764115485317810981735232251358
0.56755 51633 06957 82538	Module of ।nfinite Tetration of i		$|{}^{\infty }{i}|$	$\lim _{n\to \infty }\left|{}^{n}i\right|=\left|\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}\right|$	Mod(i^i^i^...)		ਫਰਮਾ:OEIS2C	[0;1,1,3,4,1,58,12,1,51,1,4,12,1,1,2,2,3,...]		0.56755516330695782538461314419245334
0.78343 05107 12134 40705	Sophomore's dream1 J.Bernoulli		${I}_{1}$	$\int _{0}^{1}\!x^{x}\,dx=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{n}}}={\frac {1}{1^{1}}}-{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}-{\cdots }$	Sum[n=1 to ∞] {-(-1)^n /n^n}		ਫਰਮਾ:OEIS2C	[0;1,3,1,1,1,1,1,1,2,4,7,2,1,2,1,1,1,2,1,14,...]	1697	0.78343051071213440705926438652697546
1.29128 59970 62663 54040	Sophomore's dream2 J.Bernoulli		${I}_{2}$	$\int _{0}^{1}\!{\frac {1}{x^{x}}}\,dx=\sum _{n=1}^{\infty }{\frac {1}{n^{n}}}={\frac {1}{1^{1}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{4}}}+\cdots$	Sum[n=1 to ∞] {1/(n^n)}		ਫਰਮਾ:OEIS2C	[1;3,2,3,4,3,1,2,1,1,6,7,2,5,3,1,2,1,8,1,2,4,...]	1697	1.29128599706266354040728259059560054
0.70523 01717 91800 96514	Primorial constant Sum of the product of inverse of primes		${P_{\#}}$	${\underset {p_{n}:\,{prime}}{\sum _{n=1}^{\infty }{\frac {1}{p_{n}\#}}={\frac {1}{2}}+{\frac {1}{6}}+{\frac {1}{30}}+{\frac {1}{210}}+...=\sum _{k=1}^{\infty }\prod _{n=1}^{k}{\frac {1}{p_{n}}}}}$	Sum[k=1 to ∞] (prod[n=1 to k] {1/prime(n)})	I	ਫਰਮਾ:OEIS2C	[0;1,2,2,1,1,4,1,2,1,1,6,13,1,4,1,16,6,1,1,4,...]		0.70523017179180096514743168288824851
0.14758 36176 50433 27417	Plouffe's gamma constant		${C}$	${\frac {1}{\pi }}\arctan {\frac {1}{2}}={\frac {1}{\pi }}\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2^{2n+1})(2n+1)}}$ $={\frac {1}{\pi }}\left({\frac {1}{2}}-{\frac {1}{3\cdot 2^{3}}}+{\frac {1}{5\cdot 2^{5}}}-{\frac {1}{7\cdot 2^{7}}}+\cdots \right)$	Arctan(1/2)/pi	T	ਫਰਮਾ:OEIS2C	[0;6,1,3,2,5,1,6,5,3,1,1,2,1,1,2,3,1,2,3,2,2,...]		0.14758361765043327417540107622474052
0.15915 49430 91895 33576	Plouffe's A constant		${A}$	${\frac {1}{2\pi }}$	1/(2 pi)	T	ਫਰਮਾ:OEIS2C	[0;6,3,1,1,7,2,146,3,6,1,1,2,7,5,5,1,4,1,2,42,...]		0.15915494309189533576888376337251436
0.29156 09040 30818 78013	Dimer constant 2D, Domino tiling		${\frac {C}{\pi }}$ C=Catalan	$\int \limits _{-\pi }^{\pi }{\frac {\cosh ^{-1}\left({\frac {\sqrt {\cos(t)+3}}{\sqrt {2}}}\right)}{4\pi }}\,dt$	N[int[-pi to pi] {arccosh(sqrt( cos(t)+3)/sqrt(2)) /(4*Pi)dt}]		ਫਰਮਾ:OEIS2C	[0;3,2,3,16,8,10,3,1,1,2,1,3,1,2,13,1,1,4,1,5,...]		0.29156090403081878013838445646839491
0.49801 56681 18356 04271 0.15494 98283 01810 68512 i	Factorial(i)		${i}\,!$	$\Gamma (1+i)=i\,\Gamma (i)=\int \limits _{0}^{\infty }{\frac {t^{i}}{e^{t}}}\mathrm {d} t$	Integral_0^∞ t^i/e^t dt	C	ਫਰਮਾ:OEIS2C ਫਰਮਾ:OEIS2C	[0;6,2,4,1,8,1,46,2,2,3,5,1,10,7,5,1,7,2,...] - [0;2,125,2,18,1,2,1,1,19,1,1,1,2,3,34,...] i		0.49801566811835604271369111746219809 - 0.15494982830181068512495513048388 i
2.09455 14815 42326 59148	Wallis Constant		$W$	${\sqrt[{3}]{\frac {45-{\sqrt {1929}}}{18}}}+{\sqrt[{3}]{\frac {45+{\sqrt {1929}}}{18}}}$	(((45-sqrt(1929)) /18))^(1/3)+ (((45+sqrt(1929)) /18))^(1/3)	A	ਫਰਮਾ:OEIS2C	[2;10,1,1,2,1,3,1,1,12,3,5,1,1,2,1,6,1,11,4,...]	1616 to 1703	2.09455148154232659148238654057930296
0.72364 84022 98200 00940	Sarnak constant		${C_{sa}}$	$\prod _{p>2}{\Big (}1-{\frac {p+2}{p^{3}}}{\Big )}$	N[prod[k=2 to ∞] {1-(prime(k)+2) /(prime(k)^3)}]	T ?	ਫਰਮਾ:OEIS2C	[0;1,2,1,1,1,1,1,1,1,4,4,1,1,1,1,1,1,1,8,2,1,1,...]		0.72364840229820000940884914980912759
0.63212 05588 28557 67840	Time constant		${\tau }$	$\lim _{n\to \infty }1-{\frac {!n}{n!}}=\lim _{n\to \infty }P(n)=\int _{0}^{1}e^{-x}dx=1{-}{\frac {1}{e}}=$ $\sum \limits _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n!}}={\frac {1}{1!}}{-}{\frac {1}{2!}}{+}{\frac {1}{3!}}{-}{\frac {1}{4!}}{+}{\frac {1}{5!}}{-}{\frac {1}{6!}}{+}\cdots$	lim_(n->∞) (1- !n/n!) !n=subfactorial	T	ਫਰਮਾ:OEIS2C	[0;1,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...] = [0;1,1,1,2n], n∈ℕ		0.63212055882855767840447622983853913
1.04633 50667 70503 18098	Minkowski-Siegel mass constant		$F_{1}$	$\prod _{n=1}^{\infty }{\frac {n!}{{\sqrt {2\pi n}}\left({\frac {n}{e}}\right)^{n}{\sqrt[{12}]{1+{\tfrac {1}{n}}}}}}$	N[prod[n=1 to ∞] n! /(sqrt(2*Pi*n) *(n/e)^n *(1+1/n) ^(1/12))]		ਫਰਮਾ:OEIS2C	[1;21,1,1,2,1,1,4,2,1,5,7,2,1,20,1,1,1134,3,..]	1867 1885 1935	1.04633506677050318098095065697776037
5.24411 51085 84239 62092	Lemniscate Constant		$2\varpi$	${\frac {[\Gamma ({\tfrac {1}{4}})]^{2}}{\sqrt {2\pi }}}=4\int _{0}^{1}{\frac {dx}{\sqrt {(1-x^{2})(2-x^{2})}}}$	Gamma[ 1/4 ]^2 /Sqrt[ 2 Pi ]		ਫਰਮਾ:OEIS2C	[5;4,10,2,1,2,3,29,4,1,2,1,2,1,2,1,4,9,1,4,1,2,...]	1718	5.24411510858423962092967917978223883
0.66170 71822 67176 23515	Robbins constant		$\Delta (3)$	${\frac {4\!+\!17{\sqrt {2}}\!-6{\sqrt {3}}\!-7\pi }{105}}\!+\!{\frac {\ln(1\!+\!{\sqrt {2}})}{5}}\!+\!{\frac {2\ln(2\!+\!{\sqrt {3}})}{5}}$	(4+17*2^(1/2)-6 *3^(1/2)+21*ln(1+ 2^(1/2))+42*ln(2+ 3^(1/2))-7*Pi)/105		ਫਰਮਾ:OEIS2C	[0;1,1,1,21,1,2,1,4,10,1,2,2,1,3,11,1,331,1,4,...]	1978	0.66170718226717623515583113324841358
1.30357 72690 34296 39125	Conway constant		${\lambda }$	${\begin{smallmatrix}x^{71}\quad \ -x^{69}-2x^{68}-x^{67}+2x^{66}+2x^{65}+x^{64}-x^{63}-x^{62}-x^{61}-x^{60}\\-x^{59}+2x^{58}+5x^{57}+3x^{56}-2x^{55}-10x^{54}-3x^{53}-2x^{52}+6x^{51}+6x^{50}\\+x^{49}+9x^{48}-3x^{47}-7x^{46}-8x^{45}-8x^{44}+10x^{43}+6x^{42}+8x^{41}-5x^{40}\\-12x^{39}+7x^{38}-7x^{37}+7x^{36}+x^{35}-3x^{34}+10x^{33}+x^{32}-6x^{31}-2x^{30}\\-10x^{29}-3x^{28}+2x^{27}+9x^{26}-3x^{25}+14x^{24}-8x^{23}\quad \ -7x^{21}+9x^{20}\\+3x^{19}\!-4x^{18}\!-10x^{17}\!-7x^{16}\!+12x^{15}\!+7x^{14}\!+2x^{13}\!-12x^{12}\!-4x^{11}\!-2x^{10}\\+5x^{9}+x^{7}\quad \ -7x^{6}+7x^{5}-4x^{4}+12x^{3}-6x^{2}+3x-6\ =\ 0\quad \quad \quad \end{smallmatrix}}$		A	ਫਰਮਾ:OEIS2C	[1;3,3,2,2,54,5,2,1,16,1,30,1,1,1,2,2,1,14,1,...]	1987	1.30357726903429639125709911215255189
1.18656 91104 15625 45282	Khinchin–Lévy constant		${\beta }$	${\frac {\pi ^{2}}{12\,\ln 2}}$	pi^2 /(12 ln 2)		ਫਰਮਾ:OEIS2C	[1;5,2,1,3,1,1,28,18,16,3,2,6,2,6,1,1,5,5,9,...]	1935	1.18656911041562545282172297594723712
0.83564 88482 64721 05333	Baker constant		$\beta _{3}$	$\int _{0}^{1}{\frac {\mathrm {d} t}{1+t^{3}}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{3n+1}}={\frac {1}{3}}\left(\ln 2+{\frac {\pi }{\sqrt {3}}}\right)$	Sum[n=0 to ∞] {((-1)^(n))/(3n+1)}		ਫਰਮਾ:OEIS2C	[0;1,5,11,1,4,1,6,1,4,1,1,1,2,1,3,2,2,2,2,1,3,...]		0.83564884826472105333710345970011076
23.10344 79094 20541 6160	Kempner Serie(0)		${K_{0}}$	$1{+}{\frac {1}{2}}{+}{\frac {1}{3}}{+}\cdots {+}{\frac {1}{9}}{+}{\frac {1}{11}}{+}\cdots {+}{\frac {1}{19}}{+}{\frac {1}{21}}{+}\cdots$ ${+}{\frac {1}{99}}{+}{\frac {1}{111}}{+}\cdots {+}{\frac {1}{119}}{+}{\frac {1}{121}}{+}\cdots$ (Excluding all denominators containing 0.)	1+1/2+1/3+1/4+1/5 +1/6+1/7+1/8+1/9 +1/11+1/12+1/13 +1/14+1/15+...		ਫਰਮਾ:OEIS2C	[23;9,1,2,3244,1,1,5,1,2,2,8,3,1,1,6,1,84,1,...]		23.1034479094205416160340540433255981
0.98943 12738 31146 95174	Lebesgue constant		${C_{1}}$	$\lim _{n\to \infty }\!\!\left(\!{L_{n}{-}{\frac {4}{\pi ^{2}}}\ln(2n{+}1)}\!\!\right)\!{=}{\frac {4}{\pi ^{2}}}\!\left({\sum _{k=1}^{\infty }\!{\frac {2\ln k}{4k^{2}{-}1}}}{-}{\frac {\Gamma '({\tfrac {1}{2}})}{\Gamma ({\tfrac {1}{2}})}}\!\!\right)$	4/pi^2*[(2 Sum[k=1 to ∞] {ln(k)/(4*k^2-1)}) -poligamma(1/2)]		ਫਰਮਾ:OEIS2C	[0;1,93,1,1,1,1,1,1,1,7,1,12,2,15,1,2,7,2,1,5,...]	?	0.98943127383114695174164880901886671
0.19452 80494 65325 11361	2nd du Bois-Reymond constant		${C_{2}}$	${\frac {e^{2}-7}{2}}=\int _{0}^{\infty }\left|{{\frac {d}{dt}}\left({\frac {\sin t}{t}}\right)^{n}}\right|\,dt-1$	(e^2-7)/2	T	ਫਰਮਾ:OEIS2C	[0;5,7,9,11,13,15,17,19,21,23,25,27,29,31,...] = [0;2p+3], p∈ℕ		0.19452804946532511361521373028750390
0.78853 05659 11508 96106	Lüroth constant		$C_{L}$	$\sum _{n=2}^{\infty }{\frac {\ln \left({\frac {n}{n-1}}\right)}{n}}$	Sum[n=2 to ∞] log(n/(n-1))/n		ਫਰਮਾ:OEIS2C	[0;1,3,1,2,1,2,4,1,127,1,2,2,1,3,8,1,1,2,1,16,...]		0.78853056591150896106027632216944432
1.18745 23511 26501 05459	Foias constant α		$F_{\alpha }$	$x_{n+1}=\left(1+{\frac {1}{x_{n}}}\right)^{n}{\text{ for }}n=1,2,3,\ldots$ Foias constant is the unique real number such that if x1 = α then the sequence diverges to ∞. When x1 = α, $\,\lim _{n\to \infty }x_{n}{\tfrac {\log n}{n}}=1$			ਫਰਮਾ:OEIS2C	[1;5,2,1,81,3,2,2,1,1,1,1,1,6,1,1,3,1,1,4,3,2,...]	2000	1.18745235112650105459548015839651935
2.29316 62874 11861 03150	Foias constant β		$F_{\beta }$	$x^{x+1}=(x+1)^{x}$	x^(x+1) = (x+1)^x		ਫਰਮਾ:OEIS2C	[2;3,2,2,3,4,2,3,2,130,1,1,1,1,1,6,3,2,1,15,1,...]	2000	2.29316628741186103150802829125080586
0.82246 70334 24113 21823	Nielsen-Ramanujan constant		${\frac {{\zeta }(2)}{2}}$	${\frac {\pi ^{2}}{12}}=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{2}}}={\frac {1}{1^{2}}}{-}{\frac {1}{2^{2}}}{+}{\frac {1}{3^{2}}}{-}{\frac {1}{4^{2}}}{+}{\frac {1}{5^{2}}}{-}\cdots$	Sum[n=1 to ∞] {((-1)^(n+1))/n^2}	T	ਫਰਮਾ:OEIS2C	[0;1,4,1,1,1,2,1,1,1,1,3,2,2,4,1,1,1,1,1,1,4...]	1909	0.82246703342411321823620758332301259
0.69314 71805 59945 30941	Natural logarithm of 2		$Ln(2)$	$\sum _{n=1}^{\infty }{\frac {1}{n2^{n}}}=\sum _{n=1}^{\infty }{\frac {({-}1)^{n+1}}{n}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\cdots }$	Sum[n=1 to ∞] {(-1)^(n+1)/n}	T	ਫਰਮਾ:OEIS2C	[0;1,2,3,1,6,3,1,1,2,1,1,1,1,3,10,1,1,1,2,1,1,...]	1550 to 1617	0.69314718055994530941723212145817657
0.47494 93799 87920 65033	Weierstrass constant		$\sigma ({\tfrac {1}{2}})$	${\frac {e^{\frac {\pi }{8}}{\sqrt {\pi }}}{4\cdot 2^{3/4}{({\frac {1}{4}}!)^{2}}}}$	(E^(Pi/8) Sqrt[Pi]) /(4 2^(3/4) (1/4)!^2)		ਫਰਮਾ:OEIS2C	[0;2,9,2,11,1,6,1,4,6,3,19,9,217,1,2,4,8,6...]	1872 ?	0.47494937998792065033250463632798297
0.57721 56649 01532 86060	Euler–Mascheroni constant		${\gamma }$	$\sum _{n=1}^{\infty }\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2^{n}+k}}=\sum _{n=1}^{\infty }\left({\frac {1}{n}}-\ln \left(1+{\frac {1}{n}}\right)\right)$ $=\int _{0}^{1}-\ln \left(\ln {\frac {1}{x}}\right)\,dx=-\Gamma '(1)=-\Psi (1)$	sum[n=1 to ∞] |sum[k=0 to ∞] {((-1)^k)/(2^n+k)}		ਫਰਮਾ:OEIS2C	[0;1,1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1,...]	1735	0.57721566490153286060651209008240243
1.38135 64445 18497 79337	Beta, Kneser-Mahler polynomial constant		$\beta$	$e^{^{\textstyle {\frac {2}{\pi }}\displaystyle {\int _{0}^{\frac {\pi }{3}}}\textstyle {t\tan t\ dt}}}=e^{^{\displaystyle {\,\int _{\frac {-1}{3}}^{\frac {1}{3}}}\textstyle {\,\ln \lfloor 1+e^{2\pi it}}\rfloor dt}}$	e^((PolyGamma(1,4/3) - PolyGamma(1,2/3) +9)/(4*sqrt(3)*Pi))		ਫਰਮਾ:OEIS2C	[1;2,1,1,1,1,1,4,1,139,2,1,3,5,16,2,1,1,7,2,1,...]	1963	1.38135644451849779337146695685062412
1.35845 62741 82988 43520	Golden Spiral		$c$	$\varphi ^{\frac {2}{\pi }}=\left({\frac {1+{\sqrt {5}}}{2}}\right)^{\frac {2}{\pi }}$	GoldenRatio^(2/pi)		ਫਰਮਾ:OEIS2C	[1;2,1,3,1,3,10,8,1,1,8,1,15,6,1,3,1,1,2,3,1,1,...]		1.35845627418298843520618060050187945
0.57595 99688 92945 43964	Stephens constant		$C_{S}$	$\prod _{n=1}^{\infty }\left(1-{\frac {p}{p^{3}-1}}\right)$	Prod[n=1 to ∞] {1-hprime(n) /(hprime(n)^3-1)}	T ?	ਫਰਮਾ:OEIS2C	[0;1,1,2,1,3,1,3,1,2,1,77,2,1,1,10,2,1,1,1,7,...]	?	0.57595996889294543964316337549249669
0.73908 51332 15160 64165	Dottie number		$d$	$\lim _{x\to \infty }\cos ^{[x]}(c)=\lim _{x\to \infty }\underbrace {\cos(\cos(\cos(\cdots (\cos(c)))))} _{x}$	cos(c)=c	T	ਫਰਮਾ:OEIS2C	[0;1,2,1,4,1,40,1,9,4,2,1,15,2,12,1,21,1,17,...]	?	0.73908513321516064165531208767387340
0.67823 44919 17391 97803	Taniguchi constant		$C_{T}$	$\prod _{n=1}^{\infty }\left(1-{\frac {3}{{p_{n}}^{3}}}+{\frac {2}{{p_{n}}^{4}}}+{\frac {1}{{p_{n}}^{5}}}-{\frac {1}{{p_{n}}^{6}}}\right)$ $\scriptstyle p_{n}=\,{\text{prime}}$	Prod[n=1 to ∞] {1 -3/ithprime(n)^3 +2/ithprime(n)^4 +1/ithprime(n)^5 -1/ithprime(n)^6}	T ?	ਫਰਮਾ:OEIS2C	[0;1,2,9,3,1,2,9,11,1,13,2,15,1,1,1,2,4,1,1,1,...]	?	0.67823449191739197803553827948289481
1.85407 46773 01371 91843	Gauss' Lemniscate constant		$L{\text{/}}{\sqrt {2}}$	$\int \limits _{0}^{\infty }{\frac {\mathrm {d} x}{\sqrt {1+x^{4}}}}={\frac {1}{4{\sqrt {\pi }}}}\,\Gamma \left({\frac {1}{4}}\right)^{2}={\frac {4\left({\frac {1}{4}}!\right)^{2}}{\sqrt {\pi }}}$ $\scriptstyle \Gamma (){\text{= Gamma function}}$	pi^(3/2)/(2 Gamma(3/4)^2)		ਫਰਮਾ:OEIS2C	[1;1,5,1,5,1,3,1,6,2,1,4,16,3,112,2,1,1,18,1,...]		1.85407467730137191843385034719526005
1.75874 36279 51184 82469	Infinite product constant, with Alladi-Grinstead		$Pr_{1}$	$\prod _{n=2}^{\infty }{\Big (}1+{\frac {1}{n}}{\Big )}^{\frac {1}{n}}$	Prod[n=2 to inf] {(1+1/n)^(1/n)}		ਫਰਮਾ:OEIS2C	[1;1,3,6,1,8,1,4,3,1,4,1,1,1,6,5,2,40,1,387,2,...]	1977	1.75874362795118482469989684865589317
1.86002 50792 21190 30718	Spiral of Theodorus		$\partial$	$\sum _{n=1}^{\infty }{\frac {1}{{\sqrt {n^{3}}}+{\sqrt {n}}}}=\sum _{n=1}^{\infty }{\frac {1}{{\sqrt {n}}(n+1)}}$	Sum[n=1 to ∞] {1/(n^(3/2) +n^(1/2))}		ਫਰਮਾ:OEIS2C	[1;1,6,6,1,15,11,5,1,1,1,1,5,3,3,3,2,1,1,2,19,...]	-460 to -399	1.86002507922119030718069591571714332
2.79128 78474 77920 00329	Nested radical S5		$S_{5}$	$\displaystyle {\frac {{\sqrt {21}}+1}{2}}=\scriptstyle \,{\sqrt {5+{\sqrt {5+{\sqrt {5+{\sqrt {5+{\sqrt {5+\cdots }}}}}}}}}}$ $=1+\,\scriptstyle {\sqrt {5-{\sqrt {5-{\sqrt {5-{\sqrt {5-{\sqrt {5-\cdots }}}}}}}}}}$	(sqrt(21)+1)/2	A	A222134	[2;1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,...] [2;1,3]	?	2.79128784747792000329402359686400424
0.70710 67811 86547 52440 +0.70710 67811 86547 524 i	Square root of i		${\sqrt {i}}$	${\sqrt[{4}]{-1}}={\frac {1+i}{\sqrt {2}}}=e^{\frac {i\pi }{4}}=\cos \left({\frac {\pi }{4}}\right)+i\sin \left({\frac {\pi }{4}}\right)$	(1+i)/(sqrt 2)	C A	ਫਰਮਾ:OEIS2C	[0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,..] = [0;1,2,...] [0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,..] i = [0;1,2,...] i	?	0.70710678118654752440084436210484903 + 0.70710678118654752440084436210484 i
0.80939 40205 40639 13071	Alladi–Grinstead constant		${{\mathcal {A}}_{AG}}$	$e^{-1+\sum \limits _{k=2}^{\infty }\sum \limits _{n=1}^{\infty }{\frac {1}{nk^{n+1}}}}=e^{-1-\sum \limits _{k=2}^{\infty }{\frac {1}{k}}\ln \left(1-{\frac {1}{k}}\right)}$	e^{(sum[k=2 to ∞] |sum[n=1 to ∞] {1/(n k^(n+1))})-1}		ਫਰਮਾ:OEIS2C	[0;1,4,4,17,4,3,2,5,3,1,1,1,1,6,1,1,2,1,22,...]	1977	0.80939402054063913071793188059409131
2.58498 17595 79253 21706	Sierpiński's constant		${K}$	$\pi \left(2\gamma +\ln {\frac {4\pi ^{3}}{\Gamma ({\tfrac {1}{4}})^{4}}}\right)=\pi (2\gamma +4\ln \Gamma ({\tfrac {3}{4}})-\ln \pi )$ $=\pi \left(2\ln 2+3\ln \pi +2\gamma -4\ln \Gamma ({\tfrac {1}{4}})\right)$	-Pi Log[Pi]+2 Pi EulerGamma +4 Pi Log [Gamma[3/4]]		ਫਰਮਾ:OEIS2C	[2;1,1,2,2,3,1,3,1,9,2,8,4,1,13,3,1,15,18,1,...]	1907	2.58498175957925321706589358738317116
1.73245 47146 00633 47358	Reciprocal of the Euler–Mascheroni constant		${\frac {1}{\gamma }}$	$\left(\int _{0}^{1}-\log \left(\log {\frac {1}{x}}\right)\,dx\right)^{-1}=\sum _{n=1}^{\infty }(-1)^{n}(-1+\gamma )^{n}$	1/Integrate_ {x=0 to 1} -log(log(1/x))		ਫਰਮਾ:OEIS2C	[1;1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1,11,...]		1.73245471460063347358302531586082968
1.43599 11241 76917 43235	Lebesgue constant (interpolation)		${L_{1}}$	$\prod _{\begin{smallmatrix}i=0\\j\neq i\end{smallmatrix}}^{n}{\frac {x-x_{i}}{x_{j}-x_{i}}}={\frac {1}{\pi }}\int _{0}^{\pi }{\frac {\lfloor \sin {\frac {3t}{2}}\rfloor }{\sin {\frac {t}{2}}}}\,dt={\frac {1}{3}}+{\frac {2{\sqrt {3}}}{\pi }}$	1/3 + 2*sqrt(3)/pi	T	ਫਰਮਾ:OEIS2C	[1;2,3,2,2,6,1,1,1,1,4,1,7,1,1,1,2,1,3,1,2,1,1,...]	1902 ~	1.43599112417691743235598632995927221
3.24697 96037 17467 06105	Silver root Tutte–Beraha constant		$\varsigma$	$2+2\cos {\frac {2\pi }{7}}=\textstyle 2+{\frac {2+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}{1+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}}$	2+2 cos(2Pi/7)	A	ਫਰਮਾ:OEIS2C	[3;4,20,2,3,1,6,10,5,2,2,1,2,2,1,18,1,1,3,2,...]		3.24697960371746706105000976800847962
1.94359 64368 20759 20505	Euler Totient constant		$ET$	${\underset {p{\text{= primes}}}{\prod _{p}{\Big (}1+{\frac {1}{p(p-1)}}{\Big )}}}={\frac {\zeta (2)\zeta (3)}{\zeta (6)}}={\frac {315\zeta (3)}{2\pi ^{4}}}$	zeta(2)*zeta(3) /zeta(6)		ਫਰਮਾ:OEIS2C	[1;1,16,1,2,1,2,3,1,1,3,2,1,8,1,1,1,1,1,1,1,32,...]	1750	1.94359643682075920505707036257476343
1.49534 87812 21220 54191	Fourth root of five		${\sqrt[{4}]{5}}$	${\sqrt[{5}]{5\,{\sqrt[{5}]{5\,{\sqrt[{5}]{5\,{\sqrt[{5}]{5\,{\sqrt[{5}]{5\,\cdots }}}}}}}}}}$	(5(5(5(5(5(5(5) ^1/5)^1/5)^1/5) ^1/5)^1/5)^1/5) ^1/5 ...	A	ਫਰਮਾ:OEIS2C	[1;2,53,4,96,2,1,6,2,2,2,6,1,4,1,49,17,2,3,2,...]		1.49534878122122054191189899414091339
0.87228 40410 65627 97617	Area of Ford circle		$A_{CF}$	$\sum _{q\geq 1}\sum _{(p,q)=1 \atop 1\leq p<q}\pi \left({\frac {1}{2q^{2}}}\right)^{2}{\underset {\zeta (){\text{= Riemann Zeta Function}}}{={\frac {\pi }{4}}{\frac {\zeta (3)}{\zeta (4)}}={\frac {45}{2}}{\frac {\zeta (3)}{\pi ^{3}}}}}$	pi Zeta(3) /(4 Zeta(4))			[0;1,6,1,4,1,7,5,36,3,29,1,1,10,3,2,8,1,1,1,3,...]		0.87228404106562797617519753217122587
1.08232 32337 11138 19151	Zeta(4)		$\zeta (4)$	${\frac {\pi ^{4}}{90}}=\sum _{n=1}^{\infty }{\frac {1}{n^{4}}}={\frac {1}{1^{4}}}+{\frac {1}{2^{4}}}+{\frac {1}{3^{4}}}+{\frac {1}{4^{4}}}+{\frac {1}{5^{4}}}+...$	Sum[n=1 to ∞] {1/n^4}	T	ਫਰਮਾ:OEIS2C	[1;12,6,1,3,1,4,183,1,1,2,1,3,1,1,5,4,2,7,23,...]	?	1.08232323371113819151600369654116790
1.56155 28128 08830 27491	Triangular root of 2.		${R_{2}}$	${\frac {{\sqrt {17}}-1}{2}}=\,\scriptstyle {\sqrt {4+{\sqrt {4+{\sqrt {4+{\sqrt {4+{\sqrt {4+{\sqrt {4+\cdots }}}}}}}}}}}}\,\,-1$ $=\,\scriptstyle {\sqrt {4-{\sqrt {4-{\sqrt {4-{\sqrt {4-{\sqrt {4-{\sqrt {4-\cdots }}}}}}}}}}}}\textstyle$	(sqrt(17)-1)/2	A	ਫਰਮਾ:OEIS2C	[1;1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,...] [1;1,1,3]		1.56155281280883027491070492798703851
9.86960 44010 89358 61883	Pi Squared		${\pi }^{2}$	$6\,\zeta (2)=6\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {6}{1^{2}}}+{\frac {6}{2^{2}}}+{\frac {6}{3^{2}}}+{\frac {6}{4^{2}}}+\cdots$	6 Sum[n=1 to ∞] {1/n^2}	T	A002388	[9;1,6,1,2,47,1,8,1,1,2,2,1,1,8,3,1,10,5,1,3,...]		9.86960440108935861883449099987615114
1.32471 79572 44746 02596	Plastic number		${\rho }$	${\sqrt[{3}]{1+\!{\sqrt[{3}]{1+\!{\sqrt[{3}]{1+\cdots }}}}}}=\textstyle {\sqrt[{3}]{{\frac {1}{2}}+\!{\sqrt {\frac {23}{108}}}}}+\!{\sqrt[{3}]{{\frac {1}{2}}-\!{\sqrt {\frac {23}{108}}}}}$	(1+(1+(1+(1+(1+(1) ^(1/3))^(1/3))^(1/3)) ^(1/3))^(1/3))^(1/3)	A	ਫਰਮਾ:OEIS2C	[1;3,12,1,1,3,2,3,2,4,2,141,80,2,5,1,2,8,2,...]	1929	1.32471795724474602596090885447809734
2.37313 82208 31250 90564	Lévy 2 constant		$2\,ln\,\gamma$	${\frac {\pi ^{2}}{6ln(2)}}$	Pi^(2)/(6*ln(2))	T	ਫਰਮਾ:OEIS2C	[2;2,1,2,8,57,9,32,1,1,2,1,2,1,2,1,2,1,3,2,...]	1936	2.37313822083125090564344595189447424
0.85073 61882 01867 26036	Regular paperfolding sequence		${P_{f}}$	$\sum _{n=0}^{\infty }{\frac {8^{2^{n}}}{2^{2^{n+2}}-1}}=\sum _{n=0}^{\infty }{\cfrac {\tfrac {1}{2^{2^{n}}}}{1-{\tfrac {1}{2^{2^{n+2}}}}}}$	N[Sum[n=0 to ∞] {8^2^n/(2^2^ (n+2)-1)},37]		ਫਰਮਾ:OEIS2C	[0;1,5,1,2,3,21,1,4,107,7,5,2,1,2,1,1,2,1,6,...]		0.85073618820186726036779776053206660
1.15636 26843 32269 71685	Cubic recurrence constant{{.}}		${\sigma _{3}}$	$\prod _{n=1}^{\infty }n^{{3}^{-n}}={\sqrt[{3}]{1{\sqrt[{3}]{2{\sqrt[{3}]{3\cdots }}}}}}=1^{1/3}\;2^{1/9}\;3^{1/27}\cdots$	prod[n=1 to ∞] {n ^(1/3)^n}		ਫਰਮਾ:OEIS2C	[1;6,2,1,1,8,13,1,3,2,2,6,2,1,2,1,1,1,10,33,...]		1.15636268433226971685337032288736935
1.26185 95071 42914 87419	Fractal dimension of the Koch snowflake		${C_{k}}$	${\frac {\log 4}{\log 3}}$	log(4)/log(3)	T	A100831	[1;3,1,4,1,1,11,1,46,1,5,112,1,1,1,1,1,3,1,7,...]		1.26185950714291487419905422868552171
6.58088 59910 17920 97085	Froda constant		$2^{\,e}$	$2^{e}$	2^e			[6;1,1,2,1,1,2,3,1,14,11,4,3,1,1,7,5,5,2,7,...]		6.58088599101792097085154240388648649
0.26149 72128 47642 78375	Meissel-Mertens constant		${M}$	$\lim _{n\rightarrow \infty }\!\!\left(\sum _{p\leq n}{\frac {1}{p}}\!-\ln(\ln(n))\!\right)\!\!={\underset {\!\!\!\!\gamma :\,{\text{Euler constant}},\,\,p:\,{\text{prime}}}{\!\gamma \!+\!\!\sum _{p}\!\left(\!\ln \!\left(\!1\!-\!{\frac {1}{p}}\!\right)\!\!+\!{\frac {1}{p}}\!\right)}}$	gamma+ Sum[n=1 to ∞] {ln(1-1/prime(n)) +1/prime(n)}	T ?	ਫਰਮਾ:OEIS2C	[0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,296,...]	1866 & 1873	0.26149721284764278375542683860869585
4.81047 73809 65351 65547	John constant		$\gamma$	${\sqrt[{i}]{i}}=i^{-i}=(i^{i})^{-1}=(((i)^{i})^{i})^{i}=e^{\frac {\pi }{2}}={\sqrt {\sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}}}$	e^(π/2)	T	ਫਰਮਾ:OEIS2C	[4;1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,3,2,...]		4.81047738096535165547303566670383313
-0.5 ± 0.86602 54037 84438 64676 i	Cube Root of 1		${\sqrt[{3}]{1}}$	${\begin{cases}\ \ 1\\-{\frac {1}{2}}+{\frac {\sqrt {3}}{2}}i\\-{\frac {1}{2}}-{\frac {\sqrt {3}}{2}}i.\end{cases}}$	1, E^(2i pi/3), E^(-2i pi/3)	C A	ਫਰਮਾ:OEIS2C	- [0,5] ± [0;1,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,...] i - [0,5] ± [0; 1, 6, 2] i		- 0.5 ± 0.8660254037844386467637231707529 i
0.11000 10000 00000 00000 0001	Liouville number		${\text{£}}_{Li}$	$\sum _{n=1}^{\infty }{\frac {1}{10^{n!}}}={\frac {1}{10^{1!}}}+{\frac {1}{10^{2!}}}+{\frac {1}{10^{3!}}}+{\frac {1}{10^{4!}}}+\cdots$	Sum[n=1 to ∞] {10^(-n!)}	T	ਫਰਮਾ:OEIS2C	[1;9,1,999,10,9999999999999,1,9,999,1,9]		0.11000100000000000000000100...
0.06598 80358 45312 53707	Lower limit of Tetration		${e}^{-e}$	$\left({\frac {1}{e}}\right)^{e}$	1/(e^e)		ਫਰਮਾ:OEIS2C	[0;15,6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,...]		0.06598803584531253707679018759684642
1.83928 67552 14161 13255	Tribonacci constant		${\phi _{}}_{3}$	$\textstyle {\frac {1+{\sqrt[{3}]{19+3{\sqrt {33}}}}+{\sqrt[{3}]{19-3{\sqrt {33}}}}}{3}}=\scriptstyle \,1+\left({\sqrt[{3}]{{\tfrac {1}{2}}+{\sqrt[{3}]{{\tfrac {1}{2}}+{\sqrt[{3}]{{\tfrac {1}{2}}+...}}}}}}\right)^{-1}$	(1/3)*(1+(19+3 *sqrt(33))^(1/3) +(19-3 *sqrt(33))^(1/3))	A	ਫਰਮਾ:OEIS2C	[1;1,5,4,2,305,1,8,2,1,4,6,14,3,1,13,5,1,7,...]		1.83928675521416113255185256465328660
0.36651 29205 81664 32701	Median of the Gumbel distribution		${ll_{2}}$	$-\ln(\ln(2))$	-ln(ln(2))		A074785	[0;2,1,2,1,2,6,1,6,6,2,2,2,1,12,1,8,1,1,3,1,...]		0.36651292058166432701243915823266947
36.46215 96072 07911 7709	Pi^pi		$\pi ^{\pi }$	$\pi ^{\pi }$	pi^pi		ਫਰਮਾ:OEIS2C	[36;2,6,9,2,1,2,5,1,1,6,2,1,291,1,38,50,1,2,...]		36.4621596072079117709908260226921236
0.53964 54911 90413 18711	Ioachimescu constant		$2+\zeta ({\tfrac {1}{2}})$	${2{-}(1{+}{\sqrt {2}})\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{\sqrt {n}}}}=\gamma +\sum _{n=1}^{\infty }{\frac {(-1)^{2n}\;\gamma _{n}}{2^{n}n!}}$	γ + N[ sum[n=1 to ∞] {((-1)^(2n) gamma_n) /(2^n n!)}]		2- ਫਰਮਾ:OEIS2C	[0;1,1,5,1,4,6,1,1,2,6,1,1,2,1,1,1,37,3,2,1,...]		0.53964549119041318711050084748470198
15.15426 22414 79264 1897	Exponential reiterated constant		$e^{e}$	$\sum _{n=0}^{\infty }{\frac {e^{n}}{n!}}=\lim _{n\to \infty }\left({\frac {1+n}{n}}\right)^{n^{-n}(1+n)^{1+n}}$	Sum[n=0 to ∞] {(e^n)/n!}		ਫਰਮਾ:OEIS2C	[15;6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,6,7,...]		15.1542622414792641897604302726299119
0.64624 54398 94813 30426	Masser–Gramain constant		${C}$	$\gamma {\beta }(1)\!+\!{\beta }'(1)\!=\pi \!\left(-\!\ln \Gamma ({\tfrac {1}{4}})+{\tfrac {3}{4}}\pi +{\tfrac {1}{2}}\ln 2+{\tfrac {1}{2}}\gamma \right)$ $=\pi \!\left(-\!\ln({\tfrac {1}{4}}!)+{\tfrac {3}{4}}\ln \pi -{\tfrac {3}{2}}\ln 2+{\tfrac {1}{2}}\,\gamma \right)$ $\scriptstyle \gamma ={\text{Euler–Mascheroni constant}}=0.5772156649\ldots$ $\scriptstyle \beta ()={\text{Beta function}},\quad \scriptstyle \Gamma ()={\text{Gamma function}}$	Pi/4*(2*Gamma + 2*Log[2] + 3*Log[Pi]- 4 Log[Gamma[1/4]])		ਫਰਮਾ:OEIS2C	[0;1,1,1,4,1,3,2,3,9,1,33,1,4,3,3,5,3,1,3,4,...]		0.64624543989481330426647339684579279
1.11072 07345 39591 56175	The ratio of a square and circle circumscribed		${\frac {\pi }{2{\sqrt {2}}}}$	$\sum _{n=1}^{\infty }{\frac {({-}1)^{\lfloor {\frac {n-1}{2}}\rfloor }}{2n+1}}={\frac {1}{1}}+{\frac {1}{3}}-{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}+{\frac {1}{11}}-{\cdots }$	sum[n=1 to ∞] {(-1)^(floor( (n-1)/2)) /(2n-1)}	T	ਫਰਮਾ:OEIS2C	[1;9,31,1,1,17,2,3,3,2,3,1,1,2,2,1,4,9,1,3,...]		1.11072073453959156175397024751517342
1.45607 49485 82689 67139	Backhouse's constant		${B}$	$\lim _{k\to \infty }\left|{\frac {q_{k+1}}{q_{k}}}\right\vert \quad \scriptstyle {\text{where:}}\displaystyle \;\;Q(x)={\frac {1}{P(x)}}=\!\sum _{k=1}^{\infty }q_{k}x^{k}$ $P(x)=\sum _{k=1}^{\infty }{\underset {p_{k}{\text{ prime}}}{p_{k}x^{k}}}=1+2x+3x^{2}+5x^{3}+\cdots$	1/(FindRoot[0 == 1 + Sum[x^n Prime[n], {n, 10000}], {x, {1}})		ਫਰਮਾ:OEIS2C	[1;2,5,5,4,1,1,18,1,1,1,1,1,2,13,3,1,2,4,16,...]	1995	1.45607494858268967139959535111654355
1.85193 70519 82466 17036	Gibbs constant		${Si(\pi )}$ Sin integral	$\int _{0}^{\pi }{\frac {\sin t}{t}}\,dt=\sum \limits _{n=1}^{\infty }(-1)^{n-1}{\frac {\pi ^{2n-1}}{(2n-1)(2n-1)!}}$ $=\pi -{\frac {\pi ^{3}}{3\cdot 3!}}+{\frac {\pi ^{5}}{5\cdot 5!}}-{\frac {\pi ^{7}}{7\cdot 7!}}+\cdots$	SinIntegral[Pi]		ਫਰਮਾ:OEIS2C	[1;1,5,1,3,15,1,5,3,2,7,2,1,62,1,3,110,1,39,...]		1.85193705198246617036105337015799136
0.23571 11317 19232 93137	Copeland–Erdős constant		${{\mathcal {C}}_{CE}}$	$\sum _{n=1}^{\infty }{\frac {p_{n}}{10^{n+\sum \limits _{k=1}^{n}\lfloor \log _{10}{p_{k}}\rfloor }}}$	sum[n=1 to ∞] {prime(n) /(n+(10^ sum[k=1 to n]{floor (log_10 prime(k))}))}	I	ਫਰਮਾ:OEIS2C	[0;4,4,8,16,18,5,1,1,1,1,7,1,1,6,2,9,58,1,3,...]		0.23571113171923293137414347535961677
1.52362 70862 02492 10627	Fractal dimension of the boundary of the dragon curve		${C_{d}}$	${\frac {\log \left({\frac {1+{\sqrt[{3}]{73-6{\sqrt {87}}}}+{\sqrt[{3}]{73+6{\sqrt {87}}}}}{3}}\right)}{\log(2)}}$	(log((1+(73-6 sqrt(87))^1/3+ (73+6 sqrt(87))^1/3)/3))/ log(2)))	T		[1;1,1,10,12,2,1,149,1,1,1,3,11,1,3,17,4,1,...]		1.52362708620249210627768393595421662
1.78221 39781 91369 11177	Grothendieck constant		${K_{R}}$	${\frac {\pi }{2\log(1+{\sqrt {2}})}}$	pi/(2 log(1+sqrt(2)))		ਫਰਮਾ:OEIS2C	[1;1,3,1,1,2,4,2,1,1,17,1,12,4,3,5,10,1,1,3,...]		1.78221397819136911177441345297254934
1.58496 25007 21156 18145	Hausdorff dimension, Sierpinski triangle		${log_{2}3}$	${\frac {\log 3}{\log 2}}={\frac {\sum _{n=0}^{\infty }{\frac {1}{2^{2n+1}(2n+1)}}}{\sum _{n=0}^{\infty }{\frac {1}{3^{2n+1}(2n+1)}}}}={\frac {{\frac {1}{2}}+{\frac {1}{24}}+{\frac {1}{160}}+\cdots }{{\frac {1}{3}}+{\frac {1}{81}}+{\frac {1}{1215}}+\cdots }}$	(Sum[n=0 to ∞] {1/ (2^(2n+1) (2n+1))})/ (Sum[n=0 to ∞] {1/ (3^(2n+1) (2n+1))})	T	ਫਰਮਾ:OEIS2C	[1;1,1,2,2,3,1,5,2,23,2,2,1,1,55,1,4,3,1,1,...]		1.58496250072115618145373894394781651
1.30637 78838 63080 69046	Mills' constant		${\theta }$	$\lfloor \theta ^{3^{n}}\rfloor$ primes	Nest[ NextPrime[#^3] &, 2, 7]^(1/3^8)		ਫਰਮਾ:OEIS2C	[1;3,3,1,3,1,2,1,2,1,4,2,35,21,1,4,4,1,1,3,2,...]	1947	1.30637788386308069046861449260260571
2.02988 32128 19307 25004	Figure eight knot hyperbolic volume		${V_{8}}$	$2{\sqrt {3}}\,\sum _{n=1}^{\infty }{\frac {1}{n{2n \choose n}}}\sum _{k=n}^{2n-1}{\frac {1}{k}}=6\int \limits _{0}^{\pi /3}\log \left({\frac {1}{2\sin t}}\right)\,dt=$ $\scriptstyle {\frac {\sqrt {3}}{9}}\,\sum \limits _{n=0}^{\infty }{\frac {(-1)^{n}}{27^{n}}}\,\left\{\!{\frac {18}{(6n+1)^{2}}}-{\frac {18}{(6n+2)^{2}}}-{\frac {24}{(6n+3)^{2}}}-{\frac {6}{(6n+4)^{2}}}+{\frac {2}{(6n+5)^{2}}}\!\right\}$	6 integral[0 to pi/3] {log(1/(2 sin (n)))}		ਫਰਮਾ:OEIS2C	[2;33,2,6,2,1,2,2,5,1,1,7,1,1,1,113,1,4,5,1,...]		2.02988321281930725004240510854904057
262 53741 26407 68743 .99999 99999 99250 073	Hermite–Ramanujan constant		${R}$	$e^{\pi {\sqrt {163}}}$	e^(π sqrt(163))	T	ਫਰਮਾ:OEIS2C	[262537412640768743;1,1333462407511,1,8,1,1,5,...]	1859	262537412640768743.999999999999250073
1.74540 56624 07346 86349	Khinchin harmonic mean		${K_{-1}}$	${\frac {\log 2}{\sum \limits _{n=1}^{\infty }{\frac {1}{n}}\log {\bigl (}1{+}{\frac {1}{n(n+2)}}{\bigr )}}}=\lim _{n\to \infty }{\frac {n}{{\frac {1}{a_{1}}}+{\frac {1}{a_{2}}}+\cdots +{\frac {1}{a_{n}}}}}$ a1 ... an are elements of a continued fraction [a0; a1, a2, ..., an]	(log 2)/ (sum[n=1 to ∞] {1/n log(1+ 1/(n(n+2))}		ਫਰਮਾ:OEIS2C	[1;1,2,1,12,1,5,1,5,13,2,13,2,1,9,1,6,1,3,1,...]		1.74540566240734686349459630968366106
1.64872 12707 00128 14684	Square root of the number e		${\sqrt {e}}$	$\sum _{n=0}^{\infty }{\frac {1}{2^{n}n!}}=\sum _{n=0}^{\infty }{\frac {1}{(2n)!!}}={\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{8}}+{\frac {1}{48}}+\cdots$	Sum[n=0 to ∞] {1/(2^n n!)}	T	ਫਰਮਾ:OEIS2C	[1;1,1,1,5,1,1,9,1,1,13,1,1,17,1,1,21,1,1,...] = [1;1,1,1,4p+1], p∈ℕ		1.64872127070012814684865078781416357
1.01734 30619 84449 13971	Zeta(6)		$\zeta (6)$	${\frac {\pi ^{6}}{945}}\!=\!\prod _{n=1}^{\infty }\!{\underset {p_{n}:{\text{ prime}}}{\frac {1}{{1-p_{n}}^{-6}}}}={\frac {1}{1\!-\!2^{-6}}}\!\cdot \!{\frac {1}{1\!-\!3^{-6}}}\!\cdot \!{\frac {1}{1\!-\!5^{-6}}}\cdots$	Prod[n=1 to ∞] {1/(1-ithprime (n)^-6)}	T	ਫਰਮਾ:OEIS2C	[1;57,1,1,1,15,1,6,3,61,1,5,3,1,6,1,3,3,6,1,...]		1.01734306198444913971451792979092052
0.10841 01512 23111 36151	Trott constant		$\mathrm {T} _{1}$	$\textstyle [1,0,8,4,1,0,1,5,1,2,2,3,1,1,1,3,6,...]$ ${\tfrac {1}{1+{\tfrac {1}{0+{\tfrac {1}{8+{\tfrac {1}{4+{\tfrac {1}{1+{\tfrac {1}{0+1{/\cdots }}}}}}}}}}}}}$			ਫਰਮਾ:OEIS2C	[0;9,4,2,5,1,2,2,3,1,1,1,3,6,1,5,1,1,2,...]		0.10841015122311136151129081140641509
0.00787 49969 97812 3844	Chaitin constant		$\Omega$	$\sum _{p\in P}2^{-|p|}$ p: Halted program | p |: Size in bits of program p P: Domain of all programs that stop. ਇਹ ਵੀ ਦੇਖੋ: Halting problem		T	ਫਰਮਾ:OEIS2C	[0; 126, 1, 62, 5, 5, 3, 3, 21, 1, 4, 1]	1975	0.0078749969978123844
0.83462 68416 74073 18628	Gauss constant		${G}$	${\frac {1}{\mathrm {agm} (1,{\sqrt {2}})}}={\frac {4{\sqrt {2}}\,({\tfrac {1}{4}}!)^{2}}{\pi ^{3/2}}}={\frac {2}{\pi }}\int _{0}^{1}{\frac {dx}{\sqrt {1-x^{4}}}}$ AGM = Arithmetic–geometric mean	(4 sqrt(2)((1/4)!)^2) /pi^(3/2)	T	ਫਰਮਾ:OEIS2C	[0;1,5,21,3,4,14,1,1,1,1,1,3,1,15,1,3,7,1,...]		0.83462684167407318628142973279904680
1.45136 92348 83381 05028	Ramanujan–Soldner constant		${\mu }$	$\mathrm {li} (x)=\int \limits _{0}^{x}{\frac {dt}{\ln t}}=0{\color {White}{......}}$ li = Logarithmic integral $\mathrm {li} (x)\;=\;\mathrm {Ei} (\ln {x}){\color {White}{........}}$ Ei = Exponential integral	FindRoot[li(x) = 0]	I	ਫਰਮਾ:OEIS2C	[1;2,4,1,1,1,3,1,1,1,2,47,2,4,1,12,1,1,2,2,1,...]	1792 to 1809	1.45136923488338105028396848589202744
0.64341 05462 88338 02618	Cahen's constant		$\xi _{2}$	$\sum _{k=1}^{\infty }{\frac {(-1)^{k}}{s_{k}-1}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{6}}-{\frac {1}{42}}+{\frac {1}{1806}}{\,\pm \cdots }$ Where sk is the kth term of Sylvester's sequence 2, 3, 7, 43, 1807, ... Defined as: $\,\,S_{0}=\,2,\,\,S_{k}=\,1+\prod \limits _{n=0}^{k-1}S_{n}{\text{ for}}\;k>0$		T	ਫਰਮਾ:OEIS2C	[0; 1, 1, 1, 4, 9, 196, 16641, 639988804, ...]	1891	0.64341054628833802618225430775756476
1.41421 35623 73095 04880	Square root of 2, Pythagoras constant.		${\sqrt {2}}$	$\!\prod _{n=1}^{\infty }\!\left(1\!+\!{\frac {(-1)^{n+1}}{2n-1}}\right)\!=\!\left(1\!+\!{\frac {1}{1}}\right)\!\left(1\!-\!{\frac {1}{3}}\right)\!\left(1\!+\!{\frac {1}{5}}\right)\cdots$	prod[n=1 to ∞] {1+(-1)^(n+1) /(2n-1)}	A	ਫਰਮਾ:OEIS2C	[1;2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,...] = [1;2...]		1.41421356237309504880168872420969808
1.77245 38509 05516 02729	Carlson–Levin constant		${\Gamma }({\tfrac {1}{2}})$	${\sqrt {\pi }}=\left(-{\frac {1}{2}}\right)!=\int _{-\infty }^{\infty }{\frac {1}{e^{x^{2}}}}\,dx=\int _{0}^{1}{\frac {1}{\sqrt {-\ln x}}}\,dx$	sqrt (pi)	T	ਫਰਮਾ:OEIS2C	[1;1,3,2,1,1,6,1,28,13,1,1,2,18,1,1,1,83,1,...]		1.77245385090551602729816748334114518
1.05946 30943 59295 26456	Musical interval between each half tone		${\sqrt[{12}]{2}}$	${\begin{array}{l|ccccccccccccr}\!2^{\frac {x}{12}}\!&\!\!\scriptstyle {0}&\!\!\!\!\scriptstyle {1}&\!\!\scriptstyle {2}&\!\!\scriptstyle {3}&\!\!\scriptstyle {4}&\scriptstyle {5}&\!\!\scriptstyle {6}&\!\!\scriptstyle {7}&\!\!\scriptstyle {8}&\!\!\scriptstyle {9}&\!\!\scriptstyle {10}&\!\!\scriptstyle {11}&\!\!\scriptstyle {12}\\\hline \!\scriptstyle {\textrm {Key}}\!&\!\scriptstyle {\mathrm {C_{1}} }&\!\!\scriptstyle {\mathrm {C^{\#}} }&\!\!\scriptstyle {\mathrm {D} }&\!\scriptstyle {\mathrm {D^{\#}} }&\!\!\scriptstyle {\mathrm {E} }&\scriptstyle {\mathrm {F} }&\!\scriptstyle {\mathrm {F^{\#}} }&\!\!\scriptstyle {\mathrm {G} }&\!\scriptstyle {\mathrm {G^{\#}} }&\!\!\scriptstyle {\mathrm {A} }&\!\scriptstyle {\mathrm {A^{\#}} }&\!\!\scriptstyle {\mathrm {B} }&\!\scriptstyle {\mathrm {C_{2}} }\end{array}}$(A = 440 Hz)	2^(1/12)	A	ਫਰਮਾ:OEIS2C	[1;16,1,4,2,7,1,1,2,2,7,4,1,2,1,60,1,3,1,2,...]		1.05946309435929526456182529494634170
1.01494 16064 09653 62502	Gieseking constant		${\pi \ln \beta }$	${\frac {3{\sqrt {3}}}{4}}\left(1-\sum _{n=0}^{\infty }{\frac {1}{(3n+2)^{2}}}+\sum _{n=1}^{\infty }{\frac {1}{(3n+1)^{2}}}\right)=$ $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$.	sqrt(3)*3/4 *(1 -Sum[n=0 to ∞] {1/((3n+2)^2)} +Sum[n=1 to ∞] {1/((3n+1)^2)})		ਫਰਮਾ:OEIS2C	[1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...]	1912	1.01494160640965362502120255427452028
2.62205 75542 92119 81046	Lemniscate constant		${\varpi }$	$\pi \,{G}=4{\sqrt {\tfrac {2}{\pi }}}\,\Gamma {\left({\tfrac {5}{4}}\right)^{2}}={\tfrac {1}{4}}{\sqrt {\tfrac {2}{\pi }}}\,\Gamma {\left({\tfrac {1}{4}}\right)^{2}}=4{\sqrt {\tfrac {2}{\pi }}}\left({\tfrac {1}{4}}!\right)^{2}$	4 sqrt(2/pi) ((1/4)!)^2	T	ਫਰਮਾ:OEIS2C	[2;1,1,1,1,1,4,1,2,5,1,1,1,14,9,2,6,2,9,4,1,...]	1798	2.62205755429211981046483958989111941
1.28242 71291 00622 63687	Glaisher–Kinkelin constant		${A}$	$e^{{\frac {1}{12}}-\zeta ^{\prime }(-1)}=e^{{\frac {1}{8}}-{\frac {1}{2}}\sum \limits _{n=0}^{\infty }{\frac {1}{n+1}}\sum \limits _{k=0}^{n}\left(-1\right)^{k}{\binom {n}{k}}\left(k+1\right)^{2}\ln(k+1)}$	e^(1/12-zeta´{-1})	T ?	ਫਰਮਾ:OEIS2C	[1;3,1,1,5,1,1,1,3,12,4,1,271,1,1,2,7,1,35,...]		1.28242712910062263687534256886979172
-4.22745 35333 76265 408	Digamma (1/4)		${\psi }({\tfrac {1}{4}})$	$-\gamma -{\frac {\pi }{2}}-3\ln {2}=-\gamma +\sum _{n=0}^{\infty }\left({\frac {1}{n+1}}-{\frac {1}{n+{\tfrac {1}{4}}}}\right)$	-EulerGamma -\pi/2 -3 log 2		ਫਰਮਾ:OEIS2C	-[4;4,2,1,1,10,1,5,9,11,1,22,1,1,14,1,2,1,4,...]		-4.2274535333762654080895301460966835
0.28674 74284 34478 73410	Strongly Carefree constant		$K_{2}$	$\prod _{n=1}^{\infty }{\underset {p_{n}:{\text{ prime}}}{\left(1-{\frac {3p_{n}-2}{{p_{n}}^{3}}}\right)}}={\frac {6}{\pi ^{2}}}\prod _{n=1}^{\infty }{\underset {p_{n}:{\text{ prime}}}{\left(1-{\frac {1}{p_{n}(p_{n}+1)}}\right)}}$	N[ prod[k=1 to ∞] {1-(3*prime(k)-2) /(prime(k)^3)}]		ਫਰਮਾ:OEIS2C	[0;3,2,19,3,12,1,5,1,5,1,5,2,1,1,1,1,1,3,7,...]		0.28674742843447873410789271278983845
3.62560 99082 21908 31193	Gamma(1/4)		$\Gamma ({\tfrac {1}{4}})$	$4\left({\frac {1}{4}}\right)!=\left(-{\frac {3}{4}}\right)!$	4(1/4)!	T	ਫਰਮਾ:OEIS2C	[3;1,1,1,2,25,4,9,1,1,8,4,1,6,1,1,19,1,1,4,1,...]	1729	3.62560990822190831193068515586767200
1.66168 79496 33594 12129	Somos' quadratic recurrence constant		${\sigma }$	$\prod _{n=1}^{\infty }n^{{1/2}^{n}}={\sqrt {1{\sqrt {2{\sqrt {3\cdots }}}}}}=1^{1/2}\;2^{1/4}\;3^{1/8}\cdots$	prod[n=1 to ∞] {n ^(1/2)^n}	T ?	ਫਰਮਾ:OEIS2C	[1;1,1,1,21,1,1,1,6,4,2,1,1,2,1,3,1,13,13,...]		1.66168794963359412129581892274995074
0.95531 66181 245092 78163	Magic angle		${\theta _{m}}$	$\arctan \left({\sqrt {2}}\right)=\arccos \left({\sqrt {\tfrac {1}{3}}}\right)\approx \textstyle {54.7356}^{\circ }$	arctan(sqrt(2))	T	ਫਰਮਾ:OEIS2C	[0;1,21,2,1,1,1,2,1,2,2,4,1,2,9,1,2,1,1,1,3,...]		0.95531661812450927816385710251575775
1.78107 24179 90197 98523	Exp.gamma, Barnes G-function		$e^{\gamma }$	$\prod _{n=1}^{\infty }{\frac {e^{\frac {1}{n}}}{1+{\tfrac {1}{n}}}}=\prod _{n=0}^{\infty }\left(\prod _{k=0}^{n}(k+1)^{(-1)^{k+1}{n \choose k}}\right)^{\frac {1}{n+1}}=$ $\textstyle \left({\frac {2}{1}}\right)^{1/2}\left({\frac {2^{2}}{1\cdot 3}}\right)^{1/3}\left({\frac {2^{3}\cdot 4}{1\cdot 3^{3}}}\right)^{1/4}\left({\frac {2^{4}\cdot 4^{4}}{1\cdot 3^{6}\cdot 5}}\right)^{1/5}\cdots$	Prod[n=1 to ∞] {e^(1/n)} /{1 + 1/n}		ਫਰਮਾ:OEIS2C	[1;1,3,1,1,3,5,4,1,1,2,2,1,7,9,1,16,1,1,1,2,...]		1.78107241799019798523650410310717954
0.74759 79202 53411 43517	Rényi's Parking Constant		${m}$	$\int \limits _{0}^{\infty }exp\left(\!-2\int \limits _{0}^{x}{\frac {1-e^{-y}}{y}}dy\right)\!dx={e^{-2\gamma }}\int \limits _{0}^{\infty }{\frac {e^{-2\Gamma (0,n)}}{n^{2}}}$	[e^(-2*Gamma)] *।nt{n,0,∞}[ e^(- 2 *Gamma(0,n)) /n^2]		ਫਰਮਾ:OEIS2C	[0;1,2,1,25,3,1,2,1,1,12,1,2,1,1,3,1,2,1,43,...]		0.74759792025341143517873094383017817
1.27323 95447 35162 68615	Ramanujan–Forsyth series		${\frac {4}{\pi }}$	$\displaystyle \sum \limits _{n=0}^{\infty }\textstyle \left({\frac {(2n-3)!!}{(2n)!!}}\right)^{2}={1\!+\!\left({\frac {1}{2}}\right)^{2}\!+\!\left({\frac {1}{2\cdot 4}}\right)^{2}\!+\!\left({\frac {1\cdot 3}{2\cdot 4\cdot 6}}\right)^{2}+\cdots }$	Sum[n=0 to ∞] {[(2n-3)!! /(2n)!!]^2}	I	ਫਰਮਾ:OEIS2C	[1;3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,1,1,10,...]		1.27323954473516268615107010698011489
1.44466 78610 09766 13365	Steiner number, Iterated exponential Constant		${\sqrt[{e}]{e}}$	$e^{\frac {1}{e}}{\color {White}{...........}}$ = Upper Limit of Tetration	e^(1/e)	T	ਫਰਮਾ:OEIS2C	[1;2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...]		1.44466786100976613365833910859643022
0.69220 06275 55346 35386	Minimum value of función ƒ(x) = xx		${\left({\frac {1}{e}}\right)}^{\frac {1}{e}}$	${e}^{-{\frac {1}{e}}}{\color {White}{..........}}$ =।nverse Steiner Number	e^(-1/e)		ਫਰਮਾ:OEIS2C	[0;1,2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...]		0.69220062755534635386542199718278976
0.34053 73295 50999 14282	Pólya Random walk constant		${p(3)}$	$1-\!\!\left({3 \over (2\pi )^{3}}\int \limits _{-\pi }^{\pi }\int \limits _{-\pi }^{\pi }\int \limits _{-\pi }^{\pi }{dx\,dy\,dz \over 3-\!\cos x-\!\cos y-\!\cos z}\right)^{\!-1}$ $=1-16{\sqrt {\tfrac {2}{3}}}\;\pi ^{3}\left(\Gamma ({\tfrac {1}{24}})\Gamma ({\tfrac {5}{24}})\Gamma ({\tfrac {7}{24}})\Gamma ({\tfrac {11}{24}})\right)^{-1}$	1-16*Sqrt[2/3]*Pi^3 /(Gamma[1/24] *Gamma[5/24] *Gamma[7/24] *Gamma[11/24])		ਫਰਮਾ:OEIS2C	[0;2,1,14,1,3,8,1,5,2,7,1,12,1,5,59,1,1,1,3,...]		0.34053732955099914282627318443290289
0.54325 89653 42976 70695	Bloch–Landau constant		${L}$	$={\frac {\Gamma ({\tfrac {1}{3}})\;\Gamma ({\tfrac {5}{6}})}{\Gamma ({\tfrac {1}{6}})}}={\frac {(-{\tfrac {2}{3}})!\;(-1+{\tfrac {5}{6}})!}{(-1+{\tfrac {1}{6}})!}}$	gamma(1/3) *gamma(5/6) /gamma(1/6)		ਫਰਮਾ:OEIS2C	[0;1,1,5,3,1,1,2,1,1,6,3,1,8,11,2,1,1,27,4,...]	1929	0.54325896534297670695272829530061323
0.18785 96424 62067 12024	MRB Constant, Marvin Ray Burns		$C_{{}_{MRB}}$	$\sum _{n=1}^{\infty }(-1)^{n}(n^{1/n}-1)=-{\sqrt[{1}]{1}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+\cdots$	Sum[n=1 to ∞] {(-1)^n (n^(1/n)-1)}		ਫਰਮਾ:OEIS2C	[0;5,3,10,1,1,4,1,1,1,1,9,1,1,12,2,17,2,2,1,...]	1999	0.18785964246206712024851793405427323
1.46707 80794 33975 47289	Porter Constant		${C}$	${\frac {6\ln 2}{\pi ^{2}}}\left(3\ln 2+4\,\gamma -{\frac {24}{\pi ^{2}}}\,\zeta '(2)-2\right)-{\frac {1}{2}}$ $\scriptstyle \gamma \,{\text{= Euler–Mascheroni Constant}}=0.5772156649\ldots$ $\scriptstyle \zeta '(2)\,{\text{= Derivative of }}\zeta (2)=-\sum \limits _{n=2}^{\infty }{\frac {\ln n}{n^{2}}}=-0.9375482543\ldots$	6*ln2/pi^2(3*ln2+ 4 EulerGamma- WeierstrassZeta'(2) *24/pi^2-2)-1/2		ਫਰਮਾ:OEIS2C	[1;2,7,10,1,2,38,5,4,1,4,12,5,1,5,1,2,3,1,...]	1974	1.46707807943397547289779848470722995
4.66920 16091 02990 67185	Feigenbaum constant δ		${\delta }$	$\lim _{n\to \infty }{\frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}}\qquad \scriptstyle x\in (3.8284;\,3.8495)$ $\scriptstyle x_{n+1}=\,ax_{n}(1-x_{n})\quad {\text{or}}\quad x_{n+1}=\,a\sin(x_{n})$		T	ਫਰਮਾ:OEIS2C	[4;1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5,...]	1975	4.66920160910299067185320382046620161
2.50290 78750 95892 82228	Feigenbaum constant α		$\alpha$	$\lim _{n\to \infty }{\frac {d_{n}}{d_{n+1}}}$		T ?	ਫਰਮਾ:OEIS2C	[2;1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3,...]	1979	2.50290787509589282228390287321821578
0.62432 99885 43550 87099	Golomb–Dickman constant		${\lambda }$	$\int \limits _{0}^{\infty }{\underset {{\text{Para }}x>2}{{\frac {f(x)}{x^{2}}}\,dx}}=\int \limits _{0}^{1}e^{\operatorname {Li} (n)}dn\quad \scriptstyle {\text{Li: Logarithmic integral}}$	N[Int{n,0,1}[e^Li(n)],34]		ਫਰਮਾ:OEIS2C	[0;1,1,1,1,1,22,1,2,3,1,1,11,1,1,2,22,2,6,1,...]	1930 & 1964	0.62432998854355087099293638310083724
23.14069 26327 79269 0057	Gelfond constant		${e}^{\pi }$	$(-1)^{-i}=i^{-2i}=\sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}={\frac {\pi ^{1}}{1}}+{\frac {\pi ^{2}}{2!}}+{\frac {\pi ^{3}}{3!}}+\cdots$	Sum[n=0 to ∞] {(pi^n)/n!}	T	ਫਰਮਾ:OEIS2C	[23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...]		23.1406926327792690057290863679485474
7.38905 60989 30650 22723	Conic constant, Schwarzschild constant		$e^{2}$	$\sum _{n=0}^{\infty }{\frac {2^{n}}{n!}}=1+2+{\frac {2^{2}}{2!}}+{\frac {2^{3}}{3!}}+{\frac {2^{4}}{4!}}+{\frac {2^{5}}{5!}}+\cdots$	Sum[n=0 to ∞] {2^n/n!}	T	ਫਰਮਾ:OEIS2C	[7;2,1,1,3,18,5,1,1,6,30,8,1,1,9,42,11,1,...] = [7,2,1,1,n,4*n+6,n+2], n = 3, 6, 9, etc.		7.38905609893065022723042746057500781
0.35323 63718 54995 98454	Hafner–Sarnak–McCurley constant (1)		${\sigma }$	$\prod _{k=1}^{\infty }\left\{1-[1-\prod _{j=1}^{n}{\underset {p_{k}:{\text{ prime}}}{(1-p_{k}^{-j})]^{2}}}\right\}$	prod[k=1 to ∞] {1-(1-prod[j=1 to n] {1-ithprime(k)^-j})^2}		ਫਰਮਾ:OEIS2C	[0;2,1,4,1,10,1,8,1,4,1,2,1,2,1,2,6,1,1,1,3,...]	1993	0.35323637185499598454351655043268201
0.60792 71018 54026 62866	Hafner–Sarnak–McCurley constant (2)		${\frac {1}{\zeta (2)}}$	${\frac {6}{\pi ^{2}}}=\prod _{n=0}^{\infty }{\underset {p_{n}:{\text{ prime}}}{\!\left(\!1-{\frac {1}{{p_{n}}^{2}}}\!\right)}}\!=\!\textstyle \left(1\!-\!{\frac {1}{2^{2}}}\right)\!\left(1\!-\!{\frac {1}{3^{2}}}\right)\!\left(1\!-\!{\frac {1}{5^{2}}}\right)\cdots$	Prod{n=1 to ∞} (1-1/ithprime(n)^2)	T	ਫਰਮਾ:OEIS2C	[0;1,1,1,1,4,2,4,7,1,4,2,3,4,10,1,2,1,1,1,...]		0.60792710185402662866327677925836583
0.12345 67891 01112 13141	Champernowne constant		$C_{10}$	$\sum _{n=1}^{\infty }\;\sum _{k=10^{n-1}}^{10^{n}-1}{\frac {k}{10^{kn-9\sum _{j=0}^{n-1}10^{j}(n-j-1)}}}$		T	ਫਰਮਾ:OEIS2C	[0;8,9,1,149083,1,1,1,4,1,1,1,3,4,1,1,1,15,...]	1933	0.12345678910111213141516171819202123
0.76422 36535 89220 66299	Landau-Ramanujan constant		$K$	${\frac {1}{\sqrt {2}}}\prod _{p\equiv 3\!\!\!\!\!\mod \!4}\!\!{\underset {\!\!\!\!\!\!\!\!p:{\text{ prime}}}{\left(1-{\frac {1}{p^{2}}}\right)^{-{\frac {1}{2}}}}}\!\!={\frac {\pi }{4}}\prod _{p\equiv 1\!\!\!\!\!\mod \!4}\!\!{\underset {\!\!\!\!p:{\text{ prime}}}{\left(1-{\frac {1}{p^{2}}}\right)^{\frac {1}{2}}}}$		T ?	ਫਰਮਾ:OEIS2C	[0;1,3,4,6,1,15,1,2,2,3,1,23,3,1,1,3,1,1,6,4,...]		0.76422365358922066299069873125009232
2.71828 18284 59045 23536	Number e, Euler's number		${e}$	$\!\lim _{n\to \infty }\!\left(\!1\!+\!{\frac {1}{n}}\right)^{n}\!=\!\sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1}}+{\frac {1}{2!}}+{\frac {1}{3!}}+\textstyle \cdots$	Sum[n=0 to ∞] {1/n!} (* lim_(n->∞) (1+1/n)^n *)	T	ਫਰਮਾ:OEIS2C	[2;1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...] = [2;1,2p,1], p∈ℕ		2.71828182845904523536028747135266250
0.36787 94411 71442 32159	Inverse of Number e		${\frac {1}{e}}$	$\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{n!}}={\frac {1}{0!}}-{\frac {1}{1!}}+{\frac {1}{2!}}-{\frac {1}{3!}}+{\frac {1}{4!}}-{\frac {1}{5!}}+\cdots$	Sum[n=2 to ∞] {(-1)^n/n!}	T	ਫਰਮਾ:OEIS2C	[0;2,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,...] = [0;2,1,1,2p,1], p∈ℕ	1618	0.36787944117144232159552377016146086
0.69034 71261 14964 31946	Upper iterated exponential		${H}_{2n+1}$	$\lim _{n\to \infty }{H}_{2n+1}=\textstyle \left({\frac {1}{2}}\right)^{\left({\frac {1}{3}}\right)^{\left({\frac {1}{4}}\right)^{\cdot ^{\cdot ^{\left({\frac {1}{2n+1}}\right)}}}}}={2}^{-3^{-4^{\cdot ^{\cdot ^{-2n-1}}}}}$	2^-3^-4^-5^-6^ -7^-8^-9^-10^ -11^-12^-13 …		ਫਰਮਾ:OEIS2C	[0;1,2,4,2,1,3,1,2,2,1,4,1,2,4,3,1,1,10,1,3,2,...]		0.69034712611496431946732843846418942
0.65836 55992 ...	Lower límit iterated exponential		${H}_{2n}$	$\lim _{n\to \infty }{H}_{2n}=\textstyle \left({\frac {1}{2}}\right)^{\left({\frac {1}{3}}\right)^{\left({\frac {1}{4}}\right)^{\cdot ^{\cdot ^{\left({\frac {1}{2n}}\right)}}}}}={2}^{-3^{-4^{\cdot ^{\cdot ^{-2n}}}}}$	2^-3^-4^-5^-6^ -7^-8^-9^-10^ -11^-12 …			[0;1,1,1,12,1,2,1,1,4,3,1,1,2,1,2,1,51,2,2,1,...]		0.6583655992...
3.14159 26535 89793 23846	π number, Archimedes number		$\pi$	$\lim _{n\to \infty }\,2^{n}\underbrace {\sqrt {2-{\sqrt {2+{\sqrt {2+\cdots +{\sqrt {2}}}}}}}} _{n}$	Sum[n=0 to ∞] {(-1)^n 4/(2n+1)}	T	ਫਰਮਾ:OEIS2C	[3;7,15,1,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,...]		3.14159265358979323846264338327950288
1.92878 00...	Wright constant		${\omega }$	$\left\lfloor 2^{2^{2^{\cdot ^{\cdot ^{2^{\omega }}}}}}\!\right\rfloor \scriptstyle {\text{= primes:}}\displaystyle \left\lfloor 2^{\omega }\right\rfloor \scriptstyle {\text{=3,}}\displaystyle \left\lfloor 2^{2^{\omega }}\right\rfloor \scriptstyle {\text{=13,}}\displaystyle \left\lfloor 2^{2^{2^{\omega }}}\right\rfloor \scriptstyle =16381,\ldots$			ਫਰਮਾ:OEIS2C	[1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3]		1.9287800...
0.46364 76090 00806 11621	Machin–Gregory series		$\arctan {\frac {1}{2}}$	${\underset {{\text{For }}x=1/2\qquad \qquad }{\sum _{n=0}^{\infty }{\frac {(\!-1\!)^{n}\,x^{2n+1}}{2n+1}}={\frac {1}{2}}{-}{\frac {1}{3\!\cdot \!2^{3}}}{+}{\frac {1}{5\!\cdot \!2^{5}}}{-}{\frac {1}{7\!\cdot \!2^{7}}}{+}\cdots }}$	Sum[n=0 to ∞] {(-1)^n (1/2)^(2n+1) /(2n+1)}	I	ਫਰਮਾ:OEIS2C	[0;2,6,2,1,1,1,6,1,2,1,1,2,10,1,2,1,2,1,1,1,...]		0.46364760900080611621425623146121440
0.69777 46579 64007 98200	Continued fraction constant, Bessel function		${C}_{CF}$	${\frac {I_{1}(2)}{I_{0}(2)}}={\frac {\sum \limits _{n=0}^{\infty }{\frac {n}{n!n!}}}{\sum \limits _{n=0}^{\infty }{\frac {1}{n!n!}}}}=\textstyle {\tfrac {1}{1+{\tfrac {1}{2+{\tfrac {1}{3+{\tfrac {1}{4+{\tfrac {1}{5+{\tfrac {1}{6+1{/\cdots }}}}}}}}}}}}}$	(Sum [n=0 to ∞] {n/(n!n!)}) / (Sum [n=0 to ∞] {1/(n!n!)})	I	ਫਰਮਾ:OEIS2C	[0;1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,...] = [0;p+1], p∈ℕ		0.69777465796400798200679059255175260
1.90216 05831 04	Brun 2 constant = Σ inverse of Twin primes		${B}_{\,2}$	$\textstyle {\underset {p,\,p+2:{\text{ prime}}}{\sum ({\frac {1}{p}}+{\frac {1}{p+2}})}}=({\frac {1}{3}}\!+\!{\frac {1}{5}})+({\tfrac {1}{5}}\!+\!{\tfrac {1}{7}})+({\tfrac {1}{11}}\!+\!{\tfrac {1}{13}})+\cdots$			ਫਰਮਾ:OEIS2C	[1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2]		1.902160583104
0.87058 83799 75	Brun 4 constant = Σ inv.prime quadruplets		${B}_{\,4}$	$\textstyle {\sum ({\frac {1}{p}}+{\frac {1}{p+2}}+{\frac {1}{p+6}}+{\frac {1}{p+8}})}\scriptstyle \quad {p,\;p+2,\;p+6,\;p+8:{\text{ prime}}}$ $\textstyle {\left({\tfrac {1}{5}}+{\tfrac {1}{7}}+{\tfrac {1}{11}}+{\tfrac {1}{13}}\right)}+\left({\tfrac {1}{11}}+{\tfrac {1}{13}}+{\tfrac {1}{17}}+{\tfrac {1}{19}}\right)+\dots$			ਫਰਮਾ:OEIS2C	[0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1]		0.870588379975
0.63661 97723 67581 34307	Buffon constant		${\frac {2}{\pi }}$	${\frac {\sqrt {2}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2}}}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2+{\sqrt {2}}}}}}{2}}\cdots$ Viète product	2/Pi	T	ਫਰਮਾ:OEIS2C	[0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...]	1540 to 1603	0.63661977236758134307553505349005745
0.59634 73623 23194 07434	Euler–Gompertz constant		${G}$	$\!\int \limits _{0}^{\infty }\!\!{\frac {e^{-n}}{1{+}n}}\,dn=\!\!\int \limits _{0}^{1}\!\!{\frac {1}{1{-}\ln n}}\,dn=\textstyle {\tfrac {1}{1+{\tfrac {1}{1+{\tfrac {1}{1+{\tfrac {2}{1+{\tfrac {2}{1+{\tfrac {3}{1+3{/\cdots }}}}}}}}}}}}}$	integral[0 to ∞] {(e^-n)/(1+n)}	I	ਫਰਮਾ:OEIS2C	[0;1,1,2,10,1,1,4,2,2,13,2,4,1,32,4,8,1,1,1,...]		0.59634736232319407434107849936927937
i ···	Imaginary number		${i}$	${\sqrt {-1}}={\frac {\ln(-1)}{\pi }}\qquad \qquad \mathrm {e} ^{i\,\pi }=-1$	sqrt(-1)	C I			1501 to 1576	i
2.74723 82749 32304 33305	Ramanujan nested radical		$R_{5}$	$\scriptstyle {\sqrt {5+{\sqrt {5+{\sqrt {5-{\sqrt {5+{\sqrt {5+{\sqrt {5+{\sqrt {5-\cdots }}}}}}}}}}}}}}\;=\textstyle {\frac {2+{\sqrt {5}}+{\sqrt {15-6{\sqrt {5}}}}}{2}}$	(2+sqrt(5) +sqrt(15 -6 sqrt(5)))/2	A		[2;1,2,1,21,1,7,2,1,1,2,1,2,1,17,4,4,1,1,4,2,...]		2.74723827493230433305746518613420282
0.56714 32904 09783 87299	Omega constant, Lambert W function		${\Omega }$	$\sum _{n=1}^{\infty }{\frac {(-n)^{n-1}}{n!}}=\,\left({\frac {1}{e}}\right)^{\left({\frac {1}{e}}\right)^{\cdot ^{\cdot ^{\left({\frac {1}{e}}\right)}}}}=e^{-\Omega }=e^{-e^{-e^{\cdot ^{\cdot ^{-e}}}}}$	Sum[n=1 to ∞] {(-n)^(n-1)/n!}	T	ਫਰਮਾ:OEIS2C	[0;1,1,3,4,2,10,4,1,1,1,1,2,7,306,1,5,1,2,1,...]		0.56714329040978387299996866221035555
0.96894 61462 59369 38048	Beta(3)		${\beta }(3)$	${\frac {\pi ^{3}}{32}}=\sum _{n=1}^{\infty }{\frac {-1^{n+1}}{(-1+2n)^{3}}}={\frac {1}{1^{3}}}{-}{\frac {1}{3^{3}}}{+}{\frac {1}{5^{3}}}{-}{\frac {1}{7^{3}}}{+}\cdots$	Sum[n=1 to ∞] {(-1)^(n+1) /(-1+2n)^3}	T	ਫਰਮਾ:OEIS2C	[0;1,31,4,1,18,21,1,1,2,1,2,1,3,6,3,28,1,...]		0.96894614625936938048363484584691860
2.23606 79774 99789 69640	Square root of 5, Gauss sum		${\sqrt {5}}$	$\scriptstyle (n=5)\displaystyle \sum _{k=0}^{n-1}e^{\frac {2k^{2}\pi i}{n}}=1+e^{\frac {2\pi i}{5}}+e^{\frac {8\pi i}{5}}+e^{\frac {18\pi i}{5}}+e^{\frac {32\pi i}{5}}$	Sum[k=0 to 4] {e^(2k^2 pi i/5)}	A	ਫਰਮਾ:OEIS2C	[2;4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,...] = [2;4,...]		2.23606797749978969640917366873127624
3.35988 56662 43177 55317	Prévost constant Reciprocal Fibonacci constant		$\Psi$	$\sum _{n=1}^{\infty }{\frac {1}{F_{n}}}={\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{8}}+{\frac {1}{13}}+\cdots$ Fn: Fibonacci series	Sum[n=1 to ∞] {1/Fibonacci[n]}	I	ਫਰਮਾ:OEIS2C	[3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...]	?	3.35988566624317755317201130291892717
2.68545 20010 65306 44530	Khinchin's constant		$K_{\,0}$	$\prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}\right]^{\ln n/\ln 2}$	Prod[n=1 to ∞] {(1+1/(n(n+2))) ^(ln(n)/ln(2))}	T	ਫਰਮਾ:OEIS2C	[2;1,2,5,1,1,2,1,1,3,10,2,1,3,2,24,1,3,2,...]	1934	2.68545200106530644530971483548179569

ਇਹ ਵੀ ਦੇਖੋ

• ਇਨਵੇਰੀਅੰਟ (ਗਣਿਤ)
• ਸੰਖਿਆਵਾਂ ਦੀ ਸੂਚੀ
• ਗਣਿਤਿਕ ਸਥਿਰਾਂਕ

ਬਾਹਰੀ ਲਿੰਕ

• permanent dead link] Symbolic Calculator, Plouffe's।nverter
• Constants - from Wolfram MathWorld
• On-Line Encyclopedia of।nteger Sequences (OEIS)
• Steven Finch's page of mathematical constants
• Xavier Gourdon and Pascal Sebah's page of numbers, mathematical constants and algorithms

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