गणितीय नियताङ्क

गणितीय नियताङ्क (mathematical constant) ऊ सङ्ख्या (प्रायः वास्तविक सङ्ख्या) हे जे गणितमे स्वभावतः उत्पन्न होवहे । उदाहरण - पाइ (π), आयलर सङ्ख्या, इ (e) आदि ।

नियताङ्क एवं श्रेणी

—तालिका संरचना--

• मान : नियताङ्कके सङ्ख्यात्मक मान
• लैटेक्स (LaTeX): TeX प्रारूपमे सूत्र या श्रेणी
• सूत्र: मैथमैटिका (Mathematica) या वुल्फ्रैम अल्फा (Wolfram Alpha) आदिमे प्रयोग लागि
• OEIS: On-Line Encyclopedia of Integer Sequences
• सतत भिन्न: सरल प्रारूप [to integer; frac1, frac2, frac3, ...] मे । (यदि आवर्ती होवे त कोष्टकमे)
• Nº:
  • $\mathbb {Z}$ - पूर्ण सङ्ख्या
  • $\mathbb {R} /Q$ - परिमेय सङ्ख्या
  • $\mathbb {I}$ - अपरिमेय सङ्ख्या
  • $\mathbb {T}$ - प्रागनुभविक सङ्ख्या (Transcendental number)
  • $\mathbb {C}$ - समिश्र सङ्ख्या (complex number)
  • $\mathbb {H}$-क्वाटरनीयोञ्ज (Quarternions)
  • $\mathbb {O}$ - ऑक्टोनॉट्स/ऑक्टोनीयन

(octonion)

• • $\mathbb {S}$ - sedenions

ई सूचीके 'मान', 'नाम', 'OEIS' आदि पर क्लिक करके ई सूचीके आवश्यकतानुसार क्रमित (ordered) कर सकही ।

मान	नाम	सङ्केत	लैटेक्स	सूत्र	Nº	OEIS	सतत भिन्न
3.62560990822190831193068515586767200	गामा (1/4)	$\Gamma ({\tfrac {1}{4}})$	$4\left({\frac {1}{4}}\right)!=\left(-{\frac {3}{4}}\right)!$	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)	${\theta _{m}}$	$\arctan \left({\sqrt {2}}\right)=\arccos \left({\sqrt {\tfrac {1}{3}}}\right)\approx \textstyle {54.7356}^{\circ }$	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	${e}^{\frac {1}{e}}$	$e^{\frac {1}{e}}\color {white}...........\color {black}$ = 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) = xx	${\left({\frac {1}{e}}\right)}^{\frac {1}{e}}$	${e}^{-{\frac {1}{e}}}\color {white}..........\color {black}$ = 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	${p(3)}$	$1-\!\!\left({3 \over (2\pi )^{3}}\int \limits _{-\pi }^{\pi }\int \limits _{-\pi }^{\pi }\int \limits _{-\pi }^{\pi }{dx\,dy\,dz \over 3-\!\cos x-\!\cos y-\!\cos z}\right)^{\!-1}$ $=1-16{\sqrt {\tfrac {2}{3}}}\;\pi ^{3}\left(\Gamma ({\tfrac {1}{24}})\Gamma ({\tfrac {5}{24}})\Gamma ({\tfrac {7}{24}})\Gamma ({\tfrac {11}{24}})\right)^{-1}$	1-16*Sqrt[2/3]*Pi^3 /((Gamma[1/24] *Gamma[5/24] *Gamma[7/24] *Gamma[11/24])	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	${L}$	$={\frac {\Gamma ({\tfrac {1}{3}})\;\Gamma ({\tfrac {5}{6}})}{\Gamma ({\tfrac {1}{6}})}}={\frac {(-{\tfrac {2}{3}})!\;(-1+{\tfrac {5}{6}})!}{(-1+{\tfrac {1}{6}})!}}$	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	$C_{{}_{MRB}}$	$\sum _{n=1}^{\infty }({-}1)^{n}(n^{1/n}{-}1)=-{\sqrt[{1}]{1}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+{\sqrt[{4}]{4}}\,...$	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	${m}$	$\int \limits _{0}^{\infty }exp\left(\!-2\int \limits _{0}^{x}{\frac {1-e^{-y}}{y}}dy\right)\!dx={e^{-2\gamma }}\int \limits _{0}^{\infty }{\frac {e^{-2\Gamma (0,n)}}{n^{2}}}$	[e^(-2*Gamma)] * 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	${\frac {4}{\pi }}$	$\displaystyle \sum \limits _{n=0}^{\infty }\textstyle \left({\frac {(2n-3)!!}{(2n)!!}}\right)^{2}={1\!+\!\left({\frac {1}{2}}\right)^{2}\!{+}\left({\frac {1}{2\cdot 4}}\right)^{2}\!{+}\left({\frac {1\cdot 3}{2\cdot 4\cdot 6}}\right)^{2}{+}...}$	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	${C}$	${\frac {6\ln 2}{\pi ^{2}}}\left(3\ln 2+4\,\gamma -{\frac {24}{\pi ^{2}}}\,\zeta '(2)-2\right)-{\frac {1}{2}}$ $\scriptstyle \gamma \,{\text{= Euler–Mascheroni Constant = 0,5772156649...}}$ $\scriptstyle \zeta '(2)\,{\text{= Derivative of }}\zeta (2)\,=\,-\!\!\sum \limits _{n=2}^{\infty }{\frac {\ln n}{n^{2}}}\,{\text{= −0,9375482543...}}$	6*ln2/Pi^2(3*ln2+ 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	${\delta }$	$\lim _{n\to \infty }{\frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}}\qquad \scriptstyle x\in (3,8284;\,3,8495)$ $\scriptstyle x_{n+1}=\,ax_{n}(1-x_{n})\quad {or}\quad x_{n+1}=\,a\sin(x_{n})$		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	$\alpha$	$\lim _{n\to \infty }{\frac {d_{n}}{d_{n+1}}}$		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	${\lambda }$	$\int \limits _{0}^{\infty }{\underset {Para\;x>2}{{\frac {f(x)}{x^{2}}}dx}}=\int \limits _{0}^{1}e^{Li(n)}dn\quad \scriptstyle {\text{Li: Logarithmic integral}}$	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	${e}^{\pi }$	$\sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}={\frac {\pi ^{1}}{1}}+{\frac {\pi ^{2}}{2!}}+{\frac {\pi ^{3}}{3!}}+{\frac {\pi ^{4}}{4!}}+\cdots$	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	$e^{2}$	$\sum _{n=0}^{\infty }{\frac {2^{n}}{n!}}=1+2+{\frac {2^{2}}{2!}}+{\frac {2^{3}}{3!}}+{\frac {2^{4}}{4!}}+{\frac {2^{5}}{5!}}+...$	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)	${\sigma }$	$\prod _{k=1}^{\infty }\left\{1-[1-\prod _{j=1}^{n}{\underset {p_{k}:\,{prime}}{(1-p_{k}^{-j})]^{2}}}\right\}$	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)	${\frac {1}{\zeta (2)}}$	${\frac {6}{\pi ^{2}}}{=}\prod _{n=0}^{\infty }{\underset {p_{n}:\,{prime}}{\left(1-{\frac {1}{{p_{n}}^{2}}}\right)}}{=}\textstyle \left(1{-}{\frac {1}{2^{2}}}\right)\left(1{-}{\frac {1}{3^{2}}}\right)\left(1{-}{\frac {1}{5^{2}}}\right)...$	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	${log_{2}3}$	${\frac {log3}{log2}}={\frac {\sum _{n=0}^{\infty }{\frac {1}{2^{2n+1}(2n+1)}}}{\sum _{n=0}^{\infty }{\frac {1}{3^{2n+1}(2n+1)}}}}={\frac {{\frac {1}{2}}+{\frac {1}{24}}+{\frac {1}{160}}+...}{{\frac {1}{3}}+{\frac {1}{81}}+{\frac {1}{1215}}+...}}$	(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	$C_{10}$	$\sum _{n=1}^{\infty }\;\sum _{k=10^{n-1}}^{10^{n}-1}{\frac {k}{10^{kn-9\sum _{j=0}^{n-1}10^{j}(n-j-1)}}}$		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	$K$	${\frac {1}{\sqrt {2}}}\prod _{p\equiv 3\!\!\!\!\!\mod \!4}\!\!{\underset {\!\!\!\!\!\!\!\!p:\,{prime}}{\left(1-{\frac {1}{p^{2}}}\right)^{-{\frac {1}{2}}}}}\!\!={\frac {\pi }{4}}\prod _{p\equiv 1\!\!\!\!\!\mod \!4}\!\!{\underset {\!\!\!\!p:\,{prime}}{\left(1-{\frac {1}{p^{2}}}\right)^{\frac {1}{2}}}}$		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	${\text{£}}_{Li}$	$\sum _{n=1}^{\infty }{\frac {1}{10^{n!}}}={\frac {1}{10^{1!}}}+{\frac {1}{10^{2!}}}+{\frac {1}{10^{3!}}}+{\frac {1}{10^{4!}}}+...$	Sum[n=1 to ∞] {10^(-n!)}	T	A012245	[1;9,1,999,10,9999999999999,1,9,999,1,9]
१.९२८७८००...	राइट नियताङ्क (Wright constant)	${\omega }$	$\left\lfloor 2^{2^{2^{\cdot ^{\cdot ^{2^{\omega }}}}}}\!\right\rfloor \scriptstyle {\text{= primes:}}\displaystyle \left\lfloor 2^{\omega }\right\rfloor \scriptstyle {\text{=3,}}\displaystyle \left\lfloor 2^{2^{\omega }}\right\rfloor \scriptstyle {\text{=13,}}\displaystyle \left\lfloor 2^{2^{2^{\omega }}}\right\rfloor \scriptstyle {\text{=16381, ...}}$			A086238	[1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3]
2.71828182845904523536028747135266250	Number e, Euler's number	${e}$	$\lim _{n\to \infty }\!\left(1{+}{\frac {1}{n}}\right)^{n}\!\!{=}\!\sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1}}+{\frac {1}{2!}}+{\frac {1}{3!}}+...$	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	${\frac {1}{e}}$	$\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{n!}}={\frac {1}{0!}}-{\frac {1}{1!}}+{\frac {1}{2!}}-{\frac {1}{3!}}+{\frac {1}{4!}}-{\frac {1}{5!}}+...$	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	${H}_{2n+1}$	$\lim _{n\to \infty }{H}_{2n+1}=\textstyle \left({\frac {1}{2}}\right)^{\left({\frac {1}{3}}\right)^{\left({\frac {1}{4}}\right)^{\cdot ^{\cdot ^{\left({\frac {1}{2n+1}}\right)}}}}}={2}^{-3^{-4^{\cdot ^{\cdot ^{-2n-1}}}}}$	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	${H}_{2n}$	$\lim _{n\to \infty }{H}_{2n}=\textstyle \left({\frac {1}{2}}\right)^{\left({\frac {1}{3}}\right)^{\left({\frac {1}{4}}\right)^{\cdot ^{\cdot ^{\left({\frac {1}{2n}}\right)}}}}}={2}^{-3^{-4^{\cdot ^{\cdot ^{-2n}}}}}$	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	${\frac {2}{\pi }}$	${\frac {\sqrt {2}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2}}}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2+{\sqrt {2}}}}}}{2}}\cdots$		T	A060294	[0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...]
3.14159265358979323846264338327950288	π सङ्ख्या, Archimedes number	${\pi }$	$\lim _{n\to \infty }\,2^{n}\underbrace {\sqrt {2-{\sqrt {2+{\sqrt {2+{\text{...}}+{\sqrt {2}}}}}}}} _{n}$	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	Brun 2 constant = Σ inverse of Twin primes	${B}_{\,2}$	$\textstyle {\underset {p,\,p+2:\,{prime}}{\sum ({\frac {1}{p}}+{\frac {1}{p+2}})}}=({\frac {1}{3}}{+}{\frac {1}{5}})+({\tfrac {1}{5}}{+}{\tfrac {1}{7}})+({\tfrac {1}{11}}{+}{\tfrac {1}{13}})+...$			A065421	[1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2]
0.870588379975	Brun 4 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	$\arctan {\frac {1}{2}}$	${\underset {For\;x=1/2\qquad \qquad }{\sum _{n=0}^{\infty }{\frac {(-1)^{n}x^{2n+1}}{2n+1}}={\frac {1}{2}}-\!{\frac {1}{3\cdot 2^{3}}}{+}{\frac {1}{5\cdot 2^{5}}}-\!{\frac {1}{7\cdot 2^{7}}}{+}{...}}}$	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	${G}$	$\int \limits _{0}^{\infty }{\frac {e^{-n}}{1{+}n}}dn{=}\int \limits _{0}^{1}{\frac {1}{1{-}\ln n}}dn=\textstyle {\frac {1}{1+{\frac {1}{1+{\frac {1}{1+{\frac {2}{1+{\frac {2}{1+{\frac {3}{1+{\frac {3}{1+4{/...}}}}}}}}}}}}}}}$	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	$R_{5}$	$\scriptstyle {\sqrt {5+{\sqrt {5+{\sqrt {5-{\sqrt {5+{\sqrt {5+{\sqrt {5+{\sqrt {5-\cdots }}}}}}}}}}}}}}\;=\textstyle {\frac {2+{\sqrt {5}}+{\sqrt {15-6{\sqrt {5}}}}}{2}}$	(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)	${\beta }(3)$	${\frac {\pi ^{3}}{32}}=\sum _{n=1}^{\infty }{\frac {-1^{n+1}}{(-1+2n)^{3}}}={\frac {1}{1^{3}}}{-}{\frac {1}{3^{3}}}{+}{\frac {1}{5^{3}}}{-}{\frac {1}{7^{3}}}{+}...$	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	${\sqrt {5}}$	$\scriptstyle (n=5)\displaystyle \sum _{k=0}^{n-1}e^{\frac {2k^{2}\pi i}{n}}=1+e^{\frac {2\pi i}{5}}+e^{\frac {8\pi i}{5}}+e^{\frac {18\pi i}{5}}+e^{\frac {32\pi i}{5}}$	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	$\Psi$	$\sum _{n=1}^{\infty }{\frac {1}{F_{n}}}={\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{8}}+{\frac {1}{13}}+\cdots$ Fn: 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	$K_{\,0}$	$\prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}\right]^{\ln n/\ln 2}$	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,...]

बाहरी कड़ी

• Constants - from Wolfram MathWorld
• Inverse symbolic calculator (CECM, ISC) (tells you how a given number can be constructed from mathematical constants)
• On-Line Encyclopedia of Integer Sequences (OEIS)
• Simon Plouffe's inverter
• Steven Finch's page of mathematical constants
• Xavier Gourdon and Pascal Sebah's page of numbers, mathematical constants and algorithms