गणितीय नियतांक

गणितीय नियतांक (mathematical constant) वह संख्या (प्राय: वास्तविक संख्या) है जो गणित में स्वभावत: उत्पन्न होती हैं। उदाहरण - पाई (π), आयलर संख्या ई (e) आदि।

नियतांक एवं श्रेणियाँ

—तालिका संरचना--

मान : नियतांक का संख्यात्मक मान
लैटेक्स (LaTeX): TeX प्रारूप में सूत्र या श्रेणी
सूत्र: मैथमैटिका (Mathematica) या वुल्फ्रैम अल्फा (Wolfram Alpha) आदि में प्रयोग के लिए
OEIS: On-Line Encyclopedia of Integer Sequences
सतत भिन्न: सरल प्रारूप [to integer; frac1, frac2, frac3, ...] में। (यदि आवर्ती हो तो कोष्टक में)
Nº:
- $\mathbb {Z}$ - पूर्णांक
- $\mathbb {R} /Q$ - परिमेय संख्या
- $\mathbb {I}$ - अपरिमेय संख्या
- $\mathbb {T}$ - प्रागनुभविक संख्या (Transcendental number)
- $\mathbb {C}$ - समिश्र संख्या (complex number)
- $\mathbb {H}$ -क्वाटरनीयोन्ज़ (Quarternions)
- $\mathbb {O}$ - ऑक्टोनॉट्स/ऑक्टोनीयन

(octonion)

- $\mathbb {S}$ - sedenions

इस सूची के 'मान', 'नाम', 'OEIS' आदि पर क्लिक करके इस सूची को आवश्यकतानुसार क्रमित (ordered) कर सकते हैं।

मान	नाम	संकेत	लैटेक्स	सूत्र	Nº	OEIS	सतत भिन्न
3.62560990822190831193068515586767200	गामा (1/4)^[1]	$\Gamma ({\tfrac {1}{4}})$	$4\left({\frac {1}{4}}\right)!=\left(-{\frac {3}{4}}\right)!$	Γ(1/4)!	T	A068466	[3;1,1,1,2,25,4,9,1,1,8,4,1,6,1,1,19,1,1,4,1,...]
0.95531661812450927816385710251575775	जादुई कोण (Magic angle)^[2]	${\theta _{m}}$	$\arctan \left({\sqrt {2}}\right)=\arccos \left({\sqrt {\tfrac {1}{3}}}\right)\approx \textstyle {54.7356}^{\circ }$	arctan(sqrt(2))	I	A195696	[0;1,21,2,1,1,1,2,1,2,2,4,1,2,9,1,2,1,1,1,3,...]
1.44466786100976613365833910859643022	Steiner number, Iterated Exponential Constant^[3]	${e}^{\frac {1}{e}}$	$e^{\frac {1}{e}}\color {white}...........\color {black}$ = Upper Limit of Tetration	e^(1/e)	T	A073229	[1;2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...]
0.69220062755534635386542199718278976	Minimum value of función ƒ(x) = x^x^[4]	${\left({\frac {1}{e}}\right)}^{\frac {1}{e}}$	${e}^{-{\frac {1}{e}}}\color {white}..........\color {black}$ = Inverse Steiner Number	e^(-1/e)	T	A072364	[0;1,2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...]
0.34053732955099914282627318443290289	Pólya Random Walk constant^[5]	${p(3)}$	$1-\!\!\left({3 \over (2\pi )^{3}}\int \limits _{-\pi }^{\pi }\int \limits _{-\pi }^{\pi }\int \limits _{-\pi }^{\pi }{dx\,dy\,dz \over 3-\!\cos x-\!\cos y-\!\cos z}\right)^{\!-1}$ $=1-16{\sqrt {\tfrac {2}{3}}}\;\pi ^{3}\left(\Gamma ({\tfrac {1}{24}})\Gamma ({\tfrac {5}{24}})\Gamma ({\tfrac {7}{24}})\Gamma ({\tfrac {11}{24}})\right)^{-1}$	1-16Sqrt[2/3]Pi^3 /((Gamma[1/24] Gamma[5/24] Gamma[7/24] *Gamma[11/24])	T	A086230	[0;2,1,14,1,3,8,1,5,2,7,1,12,1,5,59,1,1,1,3,...]
0.54325896534297670695272829530061323	Bloch-Landau constant^[6]	${L}$	$={\frac {\Gamma ({\tfrac {1}{3}})\;\Gamma ({\tfrac {5}{6}})}{\Gamma ({\tfrac {1}{6}})}}={\frac {(-{\tfrac {2}{3}})!\;(-1+{\tfrac {5}{6}})!}{(-1+{\tfrac {1}{6}})!}}$	gamma(1/3) *gamma(5/6) /gamma(1/6)	T	A081760	[0;1,1,5,3,1,1,2,1,1,6,3,1,8,11,2,1,1,27,4,...]
0.18785964246206712024851793405427323	MRB Constant, Marvin Ray Burns^[7]^[8]^[9]	$C_{{}_{MRB}}$	$\sum _{n=1}^{\infty }({-}1)^{n}(n^{1/n}{-}1)=-{\sqrt[{1}]{1}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+{\sqrt[{4}]{4}}\,...$	Sum[n=1 to ∞] {(-1)^n (n^(1/n)-1)}	T	A037077	[0;5,3,10,1,1,4,1,1,1,1,9,1,1,12,2,17,2,2,1,...]
0.74759792025341143517873094383017817	Rényi's Parking Constant^[10]	${m}$	$\int \limits _{0}^{\infty }exp\left(\!-2\int \limits _{0}^{x}{\frac {1-e^{-y}}{y}}dy\right)\!dx={e^{-2\gamma }}\int \limits _{0}^{\infty }{\frac {e^{-2\Gamma (0,n)}}{n^{2}}}$	[e^(-2Gamma)] Int{n,0,∞}[ e^(- 2 *Gamma(0,n)) /n^2]	T	A050996	[0;1,2,1,25,3,1,2,1,1,12,1,2,1,1,3,1,2,1,43,...]
1.27323954473516268615107010698011489	रामानुजन-फोर्सिथ श्रेणी^[11]	${\frac {4}{\pi }}$	$\displaystyle \sum \limits _{n=0}^{\infty }\textstyle \left({\frac {(2n-3)!!}{(2n)!!}}\right)^{2}={1\!+\!\left({\frac {1}{2}}\right)^{2}\!{+}\left({\frac {1}{2\cdot 4}}\right)^{2}\!{+}\left({\frac {1\cdot 3}{2\cdot 4\cdot 6}}\right)^{2}{+}...}$	Sum[n=0 to ∞] {[(2n-3)!! /(2n)!!]^2}	T	A088538	[1;3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,1,1,10,...]
1.46707807943397547289779848470722995	Porter Constant^[12]	${C}$	${\frac {6\ln 2}{\pi ^{2}}}\left(3\ln 2+4\,\gamma -{\frac {24}{\pi ^{2}}}\,\zeta '(2)-2\right)-{\frac {1}{2}}$ $\scriptstyle \gamma \,{\text{= Euler–Mascheroni Constant = 0,5772156649...}}$ $\scriptstyle \zeta '(2)\,{\text{= Derivative of }}\zeta (2)\,=\,-\!\!\sum \limits _{n=2}^{\infty }{\frac {\ln n}{n^{2}}}\,{\text{= −0,9375482543...}}$	6ln2/Pi^2(3ln2+ 4 EulerGamma- WeierstrassZeta'(2) *24/Pi^2-2)-1/2	T	A086237	[1;2,7,10,1,2,38,5,4,1,4,12,5,1,5,1,2,3,1,...]
4.66920160910299067185320382046620161	Feigenbaum constant δ^[13]	${\delta }$	$\lim _{n\to \infty }{\frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}}\qquad \scriptstyle x\in (3,8284;\,3,8495)$ $\scriptstyle x_{n+1}=\,ax_{n}(1-x_{n})\quad {or}\quad x_{n+1}=\,a\sin(x_{n})$		T	A006890	[4;1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5,...]
2.50290787509589282228390287321821578	Feigenbaum constant α^[14]	$\alpha$	$\lim _{n\to \infty }{\frac {d_{n}}{d_{n+1}}}$		T	A006891	[2;1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3,...]
0.62432998854355087099293638310083724	Golomb–Dickman constant^[15]	${\lambda }$	$\int \limits _{0}^{\infty }{\underset {Para\;x>2}{{\frac {f(x)}{x^{2}}}dx}}=\int \limits _{0}^{1}e^{Li(n)}dn\quad \scriptstyle {\text{Li: Logarithmic integral}}$	N[Int{n,0,1}[e^Li(n)],34]	T	A084945	[0;1,1,1,1,1,22,1,2,3,1,1,11,1,1,2,22,2,6,1,...]
23.1406926327792690057290863679485474	Gelfond constant^[16]	${e}^{\pi }$	$\sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}={\frac {\pi ^{1}}{1}}+{\frac {\pi ^{2}}{2!}}+{\frac {\pi ^{3}}{3!}}+{\frac {\pi ^{4}}{4!}}+\cdots$	Sum[n=0 to ∞] {(pi^n)/n!}	T	A039661	[23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...]
7.38905609893065022723042746057500781	शंकु नियतांक (Conic constant), Schwarzschild constant^[17]	$e^{2}$	$\sum _{n=0}^{\infty }{\frac {2^{n}}{n!}}=1+2+{\frac {2^{2}}{2!}}+{\frac {2^{3}}{3!}}+{\frac {2^{4}}{4!}}+{\frac {2^{5}}{5!}}+...$	Sum[n=0 to ∞] {2^n/n!}	T	A072334	[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.
0.35323637185499598454351655043268201	Hafner-Sarnak-McCurley constant (1)^[18]	${\sigma }$	$\prod _{k=1}^{\infty }\left\{1-[1-\prod _{j=1}^{n}{\underset {p_{k}:\,{prime}}{(1-p_{k}^{-j})]^{2}}}\right\}$	prod[k=1 to ∞] {1-(1-prod[j=1 to n] {1-ithprime(k)^-j})^2}	T	A085849	[0;2,1,4,1,10,1,8,1,4,1,2,1,2,1,2,6,1,1,1,3,...]
0.60792710185402662866327677925836583	Hafner-Sarnak-McCurley constant (2)^[19]	${\frac {1}{\zeta (2)}}$	${\frac {6}{\pi ^{2}}}{=}\prod _{n=0}^{\infty }{\underset {p_{n}:\,{prime}}{\left(1-{\frac {1}{{p_{n}}^{2}}}\right)}}{=}\textstyle \left(1{-}{\frac {1}{2^{2}}}\right)\left(1{-}{\frac {1}{3^{2}}}\right)\left(1{-}{\frac {1}{5^{2}}}\right)...$	Prod{n=1 to ∞} (1-1/ithprime (n)^2)	T	A059956	[0;1,1,1,1,4,2,4,7,1,4,2,3,4,10,1,2,1,1,1,...]
1.58496250072115618145373894394781651	Hausdorff dimension, Sierpinski triangle^[20]	${log_{2}3}$	${\frac {log3}{log2}}={\frac {\sum _{n=0}^{\infty }{\frac {1}{2^{2n+1}(2n+1)}}}{\sum _{n=0}^{\infty }{\frac {1}{3^{2n+1}(2n+1)}}}}={\frac {{\frac {1}{2}}+{\frac {1}{24}}+{\frac {1}{160}}+...}{{\frac {1}{3}}+{\frac {1}{81}}+{\frac {1}{1215}}+...}}$	(Sum[n=0 to ∞] {1/ (2^(2n+1) (2n+1))})/ (Sum[n=0 to ∞] {1/ (3^(2n+1) (2n+1))})	T	A020857	[1;1,1,2,2,3,1,5,2,23,2,2,1,1,55,1,4,3,1,1,...]
0.12345678910111213141516171819202123	Champernowne constant^[21]	$C_{10}$	$\sum _{n=1}^{\infty }\;\sum _{k=10^{n-1}}^{10^{n}-1}{\frac {k}{10^{kn-9\sum _{j=0}^{n-1}10^{j}(n-j-1)}}}$		T	A033307	[0;8,9,1,149083,1,1,1,4,1,1,1,3,4,1,1,1,15,...]
0.76422365358922066299069873125009232	Landau-Ramanujan constant^[22]	$K$	${\frac {1}{\sqrt {2}}}\prod _{p\equiv 3\!\!\!\!\!\mod \!4}\!\!{\underset {\!\!\!\!\!\!\!\!p:\,{prime}}{\left(1-{\frac {1}{p^{2}}}\right)^{-{\frac {1}{2}}}}}\!\!={\frac {\pi }{4}}\prod _{p\equiv 1\!\!\!\!\!\mod \!4}\!\!{\underset {\!\!\!\!p:\,{prime}}{\left(1-{\frac {1}{p^{2}}}\right)^{\frac {1}{2}}}}$		T	A064533	[0;1,3,4,6,1,15,1,2,2,3,1,23,3,1,1,3,1,1,6,4,...]
0.11000100000000000000000100...	Liouville number^[23]	${\text{£}}_{Li}$	$\sum _{n=1}^{\infty }{\frac {1}{10^{n!}}}={\frac {1}{10^{1!}}}+{\frac {1}{10^{2!}}}+{\frac {1}{10^{3!}}}+{\frac {1}{10^{4!}}}+...$	Sum[n=1 to ∞] {10^(-n!)}	T	A012245	[1;9,1,999,10,9999999999999,1,9,999,1,9]
१.९२८७८००...	राइट नियतांक (Wright constant)^[24]	${\omega }$	$\left\lfloor 2^{2^{2^{\cdot ^{\cdot ^{2^{\omega }}}}}}\!\right\rfloor \scriptstyle {\text{= primes:}}\displaystyle \left\lfloor 2^{\omega }\right\rfloor \scriptstyle {\text{=3,}}\displaystyle \left\lfloor 2^{2^{\omega }}\right\rfloor \scriptstyle {\text{=13,}}\displaystyle \left\lfloor 2^{2^{2^{\omega }}}\right\rfloor \scriptstyle {\text{=16381, ...}}$			A086238	[1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3]
2.71828182845904523536028747135266250	Number e, Euler's number^[25]	${e}$	$\lim _{n\to \infty }\!\left(1{+}{\frac {1}{n}}\right)^{n}\!\!{=}\!\sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1}}+{\frac {1}{2!}}+{\frac {1}{3!}}+...$	Sum[n=0 to ∞] {1/n!}	T	A001113	[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
0.36787944117144232159552377016146086	Reverse of Number e^[26]	${\frac {1}{e}}$	$\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{n!}}={\frac {1}{0!}}-{\frac {1}{1!}}+{\frac {1}{2!}}-{\frac {1}{3!}}+{\frac {1}{4!}}-{\frac {1}{5!}}+...$	Sum[n=2 to ∞] {(-1)^n/n!}	T	A068985	[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
0.6903471261...	Upper iterated exponential^[27]	${H}_{2n+1}$	$\lim _{n\to \infty }{H}_{2n+1}=\textstyle \left({\frac {1}{2}}\right)^{\left({\frac {1}{3}}\right)^{\left({\frac {1}{4}}\right)^{\cdot ^{\cdot ^{\left({\frac {1}{2n+1}}\right)}}}}}={2}^{-3^{-4^{\cdot ^{\cdot ^{-2n-1}}}}}$	2^-3^-4^-5^-6^ -7^-8^-9^-10^ -11^-12^-13 …	T		[0;1,2,4,2,1,3,1,2,2,1,4,1,2,4,61,5,...]
0.6583655992...	Lower límit iterated exponential^[28]	${H}_{2n}$	$\lim _{n\to \infty }{H}_{2n}=\textstyle \left({\frac {1}{2}}\right)^{\left({\frac {1}{3}}\right)^{\left({\frac {1}{4}}\right)^{\cdot ^{\cdot ^{\left({\frac {1}{2n}}\right)}}}}}={2}^{-3^{-4^{\cdot ^{\cdot ^{-2n}}}}}$	2^-3^-4^-5^-6^ -7^-8^-9^-10^ -11^-12 …	T		[0;1,1,1,12,1,2,1,1,4,3,1,1,2,1,2,1,51,2,2,1,...]
0.63661977236758134307553505349005745	२/π, François Viète product^[29]	${\frac {2}{\pi }}$	${\frac {\sqrt {2}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2}}}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2+{\sqrt {2}}}}}}{2}}\cdots$		T	A060294	[0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...]
3.14159265358979323846264338327950288	π संख्या, Archimedes number^[30]	${\pi }$	$\lim _{n\to \infty }\,2^{n}\underbrace {\sqrt {2-{\sqrt {2+{\sqrt {2+{\text{...}}+{\sqrt {2}}}}}}}} _{n}$	Sum[n=0 to ∞] {(-1)^n 4/(2n+1)}	T	A000796	[3;7,15,1,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,...]
1.902160583104	Brun₂ constant = Σ inverse of Twin primes^[31]	${B}_{\,2}$	$\textstyle {\underset {p,\,p+2:\,{prime}}{\sum ({\frac {1}{p}}+{\frac {1}{p+2}})}}=({\frac {1}{3}}{+}{\frac {1}{5}})+({\tfrac {1}{5}}{+}{\tfrac {1}{7}})+({\tfrac {1}{11}}{+}{\tfrac {1}{13}})+...$			A065421	[1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2]
0.870588379975	Brun₄ constant = Σ inv.prime quadruplets	${B}_{\,4}$	$\textstyle {\sum ({\frac {1}{p}}+{\frac {1}{p+2}}+{\frac {1}{p+4}}+{\frac {1}{p+6}})}\scriptstyle \quad {p,\;p+2,\;p+4,\;p+6:\;{prime}}$ $\textstyle {\left({\tfrac {1}{5}}+{\tfrac {1}{7}}+{\tfrac {1}{11}}+{\tfrac {1}{13}}\right)}+\left({\tfrac {1}{11}}+{\tfrac {1}{13}}+{\tfrac {1}{17}}+{\tfrac {1}{19}}\right)+\dots$			A213007	[0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1]
0.46364760900080611621425623146121440	Machin-Gregory serie^[32]	$\arctan {\frac {1}{2}}$	${\underset {For\;x=1/2\qquad \qquad }{\sum _{n=0}^{\infty }{\frac {(-1)^{n}x^{2n+1}}{2n+1}}={\frac {1}{2}}-\!{\frac {1}{3\cdot 2^{3}}}{+}{\frac {1}{5\cdot 2^{5}}}-\!{\frac {1}{7\cdot 2^{7}}}{+}{...}}}$	Sum[n=0 to ∞] {(-1)^n (1/2)^(2n+1)/(2n+1)}	T	A073000	[0;2,6,2,1,1,1,6,1,2,1,1,2,10,1,2,1,2,1,1,1,...]
0.59634736232319407434107849936927937	Euler-Gompertz constant^[33]	${G}$	$\int \limits _{0}^{\infty }{\frac {e^{-n}}{1{+}n}}dn{=}\int \limits _{0}^{1}{\frac {1}{1{-}\ln n}}dn=\textstyle {\frac {1}{1+{\frac {1}{1+{\frac {1}{1+{\frac {2}{1+{\frac {2}{1+{\frac {3}{1+{\frac {3}{1+4{/...}}}}}}}}}}}}}}}$	integral[0 to ∞] {(e^-n)/(1+n)}	T	A073003	[0;1,1,2,10,1,1,4,2,2,13,2,4,1,32,4,8,1,1,1,...]
0.69777465796400798200679059255175260	Continued fraction constant, Bessel function	${C}_{CF}$	${\frac {I_{1}(2)}{I_{0}(2)}}={\frac {\sum \limits _{n=0}^{\infty }{\frac {n}{n!n!}}}{\sum \limits _{n=0}^{\infty }{\frac {1}{n!n!}}}}=\textstyle {\frac {1}{1+{\frac {1}{2+{\frac {1}{3+{\frac {1}{4+{\frac {1}{5+{\frac {1}{6+1{/...}}}}}}}}}}}}}$	(Sum [n=0 to ∞] {n/(n!n!)}) / (Sum [n=0 to ∞] {1/(n!n!)})		A052119	[0;1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,...] = [0;(p+1)], p∈ℕ
0.43828293672703211162697516355126482 + 0.36059247187138548595294052690600 i	अनंत टिट्रेशन/Tetration i का	${}^{\infty }{i}$	$\lim _{n\to \infty }{}^{n}i=\lim _{n\to \infty }\underbrace {i^{i^{i^{\cdot ^{\cdot ^{i}}}}}} _{n}={\underset {W:\;Lambert\;function}{{\frac {2}{\pi }}\,i\;W\left(-{\frac {\pi }{2}}i\right)}}$	(2/Pi) i ProductLog[-((Pi/2) i)]	C	A077589 A077590	[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
2.74723827493230433305746518613420282	Ramanujan nested radical^[34]	$R_{5}$	$\scriptstyle {\sqrt {5+{\sqrt {5+{\sqrt {5-{\sqrt {5+{\sqrt {5+{\sqrt {5+{\sqrt {5-\cdots }}}}}}}}}}}}}}\;=\textstyle {\frac {2+{\sqrt {5}}+{\sqrt {15-6{\sqrt {5}}}}}{2}}$	(2+sqrt(5) +sqrt(15 -6 sqrt(5)))/2	I		[2;1,2,1,21,1,7,2,1,1,2,1,2,1,17,4,4,1,1,4,2,...]
1.01494160640965362502120255427452028	Gieseking constant	${\pi \ln \beta }$	${\frac {3{\sqrt {3}}}{4}}\left(1-\sum _{n=0}^{\infty }{\frac {1}{(3n+2)^{2}}}+\sum _{n=1}^{\infty }{\frac {1}{(3n+1)^{2}}}\right)=$ $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm ...\right)$ .	sqrt(3)3/4 (1 -Sum[n=0 to ∞] {1/((3n+2)^2)} +Sum[n=1 to ∞] {1/((3n+1)^2)})	T	A143298	[1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...]
1.66168794963359412129581892274995074	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	A065481	[1;1,1,1,21,1,1,1,6,4,2,1,1,2,1,3,1,13,13,...]
0.56714329040978387299996866221035555	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!}		A030178	[0;1,1,3,4,2,10,4,1,1,1,1,2,7,306,1,5,1,2,1,...]
0.96894614625936938048363484584691860	Beta(3)^[35]	${\beta }(3)$	${\frac {\pi ^{3}}{32}}=\sum _{n=1}^{\infty }{\frac {-1^{n+1}}{(-1+2n)^{3}}}={\frac {1}{1^{3}}}{-}{\frac {1}{3^{3}}}{+}{\frac {1}{5^{3}}}{-}{\frac {1}{7^{3}}}{+}...$	Sum[n=1 to ∞] {(-1)^(n+1) /(-1+2n)^3}	T	A153071	[0;1,31,4,1,18,21,1,1,2,1,2,1,3,6,3,28,1,...]
2.23606797749978969640917366873127624	Square root of 5, Gauss sum^[36]	${\sqrt {5}}$	$\scriptstyle (n=5)\displaystyle \sum _{k=0}^{n-1}e^{\frac {2k^{2}\pi i}{n}}=1+e^{\frac {2\pi i}{5}}+e^{\frac {8\pi i}{5}}+e^{\frac {18\pi i}{5}}+e^{\frac {32\pi i}{5}}$	Sum[k=0 to 4] {e^(2k^2 pi i/5)}	I	A002163	[2;4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,...] = [2;(4),...]
3.35988566624317755317201130291892717	Prévost constant	$\Psi$	$\sum _{n=1}^{\infty }{\frac {1}{F_{n}}}={\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{8}}+{\frac {1}{13}}+\cdots$ F_n: Fibonacci series	Sum[n=1 to ∞] {1/Fibonacci[n]}	I	A079586	[3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...]
2.68545200106530644530971483548179569	Khinchin's constant^[37]	$K_{\,0}$	$\prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}\right]^{\ln n/\ln 2}$	Prod[n=1 to ∞] {(1+1/(n(n+2))) ^(ln(n)/ln(2))}	?	A002210	[2;1,2,5,1,1,2,1,1,3,10,2,1,3,2,24,1,3,2,...]