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:
 - पूर्णांक
  - परिमेय संख्या
  - अपरिमेय संख्या
  - प्रागनुभविक संख्या (Transcendental number)
  - समिश्र संख्या (complex number)
 -क्वाटरनीयोन्ज़ (Quarternions)
  - ऑक्टोनॉट्स/ऑक्टोनीयन 
(octonion)
  - 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) Γ(1/4)!TA068466[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)arctan(sqrt(2))IA195696[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 = Upper Limit of Tetratione^(1/e)TA073229 [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 = Inverse Steiner Number e^(-1/e)TA072364 [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 constant1-16*Sqrt[2/3]*Pi^3 /((Gamma[1/24]*Gamma[5/24]*Gamma[7/24]*Gamma[11/24]) TA086230[0;2,1,14,1,3,8,1,5,2,7,1,12,1,5,59,1,1,1,3,...] 0.54325896534297670695272829530061323  Bloch-Landau constantgamma(1/3)*gamma(5/6)/gamma(1/6)TA081760[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 BurnsSum[n=1 to ∞]{(-1)^n (n^(1/n)-1)} TA037077[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 [e^(-2*Gamma)] * Int{n,0,∞}[ e^(- 2*Gamma(0,n)) /n^2]TA050996[0;1,2,1,25,3,1,2,1,1,12,1,2,1,1,3,1,2,1,43,...] 1.27323954473516268615107010698011489  रामानुजन-फोर्सिथ श्रेणीSum[n=0 to ∞]  {[(2n-3)!!  /(2n)!!]^2}TA088538[1;3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,1,1,10,...] 1.46707807943397547289779848470722995  Porter Constant  6*ln2/Pi^2(3*ln2+ 4 EulerGamma- WeierstrassZeta'(2) *24/Pi^2-2)-1/2 TA086237[1;2,7,10,1,2,38,5,4,1,4,12,5,1,5,1,2,3,1,...] 4.66920160910299067185320382046620161  Feigenbaum constant δTA006890[4;1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5,...] 2.50290787509589282228390287321821578  Feigenbaum constant αTA006891[2;1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3,...] 0.62432998854355087099293638310083724  Golomb–Dickman constantN[Int{n,0,1}[e^Li(n)],34]TA084945[0;1,1,1,1,1,22,1,2,3,1,1,11,1,1,2,22,2,6,1,...] 23.1406926327792690057290863679485474  Gelfond constantSum[n=0 to ∞]  {(pi^n)/n!}TA039661[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 Sum[n=0 to ∞]{2^n/n!}TA072334[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)prod[k=1 to ∞] {1-(1-prod[j=1 to n] {1-ithprime(k)^-j})^2} TA085849[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)Prod{n=1 to ∞}(1-1/ithprime(n)^2) TA059956[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(Sum[n=0 to ∞] {1/(2^(2n+1) (2n+1))})/  (Sum[n=0 to ∞] {1/(3^(2n+1) (2n+1))})TA020857[1;1,1,2,2,3,1,5,2,23,2,2,1,1,55,1,4,3,1,1,...] 0.12345678910111213141516171819202123  Champernowne constantTA033307[0;8,9,1,149083,1,1,1,4,1,1,1,3,4,1,1,1,15,...] 0.76422365358922066299069873125009232  Landau-Ramanujan constantTA064533[0;1,3,4,6,1,15,1,2,2,3,1,23,3,1,1,3,1,1,6,4,...]0.11000100000000000000000100...Liouville numberSum[n=1 to ∞]  {10^(-n!)}TA012245[1;9,1,999,10,9999999999999,1,9,999,1,9]१.९२८७८००...राइट नियतांक (Wright constant)A086238[1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3] 2.71828182845904523536028747135266250  Number e, Euler's numberSum[n=0 to ∞]{1/n!}  TA001113[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 eSum[n=2 to ∞]{(-1)^n/n!}TA068985[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∈ℕ0.6903471261... Upper iterated exponential 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
  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 productTA060294[0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...] 3.14159265358979323846264338327950288   π संख्या, Archimedes numberSum[n=0 to ∞]{(-1)^n 4/(2n+1)} TA000796[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 primesA065421[1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2]0.870588379975 Brun 4  constant = Σ inv.prime quadruplets A213007[0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1] 0.46364760900080611621425623146121440  Machin-Gregory serieSum[n=0 to ∞]  {(-1)^n (1/2)^(2n+1)/(2n+1)}TA073000[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 constantintegral[0 to ∞]{(e^-n)/(1+n)}TA073003[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(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   अनंतटिट्रेशन/Tetration i का(2/Pi) i ProductLog[-((Pi/2) i)]CA077589  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(2+sqrt(5)+sqrt(15-6 sqrt(5)))/2I[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  
.sqrt(3)*3/4 *(1-Sum[n=0 to ∞]{1/((3n+2)^2)}+Sum[n=1 to ∞]{1/((3n+1)^2)})TA143298[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 prod[n=1 to ∞]{n ^(1/2)^n}TA065481 [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 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) Sum[n=1 to ∞]{(-1)^(n+1)/(-1+2n)^3}TA153071[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 sumSum[k=0 to 4]{e^(2k^2 pi i/5)}IA002163[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 constantFn: Fibonacci seriesSum[n=1 to ∞]{1/Fibonacci[n]}IA079586[3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...] 2.68545200106530644530971483548179569  Khinchin's constantProd[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,...]

 सन्दर्भ 

 बाहरी कड़ियाँ 
 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

श्रेणी:गणित
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