This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A203138 #31 Apr 21 2024 11:40:24 %S A203138 2,3,4,6,2,4,8,7,6,9,3,1,8,3,3,1,9,8,8,1,3,8,5,7,1,1,4,6,9,5,8,6,2,9, %T A203138 4,9,3,0,4,3,3,3,6,5,1,3,4,0,0,4,6,1,0,1,6,4,7,3,9,7,9,8,4,7,5,8,2,5, %U A203138 1,5,0,1,1,4,0,1,8,3,9,7,7,6,9,4,3,4,9,9,1,7,4,6,5,9,4,9,5,9,7 %N A203138 Decimal expansion of Gamma(1/24). %C A203138 In the article by Vidunas, the third formula on page 13 is wrong. The exponent of the term K((sqrt(3)-1)/(2*sqrt(2)))^(1/3) is wrong. It should be Gamma(1/24) = Pi^(1/24) * 2^(89/36) * 3^(25/48) * sqrt(1+sqrt(2)) * (sqrt(3)-1)^(1/4) * K(1/sqrt(2))^(1/4) * K((sqrt(3)-1)/(2*sqrt(2)))^(1/6) * K((2-sqrt(3))*(sqrt(3)-sqrt(2)))^(1/2). - _Vaclav Kotesovec_, Apr 21 2024 %H A203138 G. C. Greubel, <a href="/A203138/b203138.txt">Table of n, a(n) for n = 2..5002</a> %H A203138 R. Vidunas, <a href="http://arxiv.org/abs/math/0403510">Expressions for values of the Gamma function</a>, arxiv:math/0403510 [math.CA], 2004. %H A203138 <a href="/index/Ga#gamma_function">Index to sequences related to gamma function</a> %F A203138 From _Vaclav Kotesovec_, Apr 21 2024: (Start) %F A203138 Equals 2^(13/12) * 3^(9/16) * Pi^(1/4) * (sqrt(3) - 1)^(1/4) * sqrt((1 + sqrt(2)) * Gamma(1/3) * Gamma(1/4)) * EllipticTheta(3, 0, exp(-Pi*sqrt(6))). %F A203138 Equals 2^(35/24) * 3^(3/8) * sqrt(Pi*(1 + sqrt(2)) * Gamma(1/12) / (1 + sqrt(3))) * EllipticTheta(3, 0, exp(-Pi*sqrt(6))). (End) %e A203138 23.462487693183319881385711469586294930433365134004610164739... %p A203138 evalf(GAMMA(1/24), 110); # _Vaclav Kotesovec_, Apr 21 2024 %p A203138 evalf(Pi^(1/24) * 2^(89/36) * 3^(25/48) * sqrt(1+sqrt(2)) * (sqrt(3)-1)^(1/4) * EllipticK(1/sqrt(2))^(1/4) * EllipticK((sqrt(3)-1)/(2*sqrt(2)))^(1/6) * EllipticK((2-sqrt(3))*(sqrt(3)-sqrt(2)))^(1/2), 110); # _Vaclav Kotesovec_, Apr 21 2024 %t A203138 RealDigits[Gamma[1/24], 10, 100][[1]] (* _G. C. Greubel_, Mar 10 2018 *) %o A203138 (PARI) default(realprecision, 100); gamma(1/24) \\ _G. C. Greubel_, Mar 10 2018 %o A203138 (Magma) SetDefaultRealField(RealField(100)); Gamma(1/24); // _G. C. Greubel_, Mar 10 2018 %K A203138 nonn,cons %O A203138 2,1 %A A203138 _N. J. A. Sloane_, Dec 29 2011