गणितीय नियतांक

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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[संपादित करें]

—तालिका संरचना--

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

मान नाम संकेत LaTeX सूत्र OEIS सतत भिन्न
3.62560990822190831193068515586767200 गामा (1/4)[1] 4(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] 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] = 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[4]
= 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]

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[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] 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] [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[11] 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]

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[13]

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] 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] 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] 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] 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] 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] 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] (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] 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] 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] Sum[n=1 to ∞]
{10^(-n!)}
T A012245 [1;9,1,999,10,9999999999999,1,9,999,1,9]
1.9287800... राइट नियतांक (Wright constant)[24] A086238 [1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3]
2.71828182845904523536028747135266250 Number e, Euler's number[25] 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] 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] 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] 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 2/Pi, François Viète product[29] T A060294 [0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...]
3.14159265358979323846264338327950288 π number, Archimedes number[30] 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[31] A065421 [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 serie[32] 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] 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 (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
Infinite
Tetration
of i
(2/Pi) i ProductLog[-((Pi/2) i)] 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] (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

.

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 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 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] 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] 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

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[37] 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,...]

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बाहरी कड़ियाँ[संपादित करें]