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%I #31 Apr 15 2024 08:08:51
%S 7,5,3,3,9,4,1,5,9,8,7,9,7,6,1,1,9,0,4,6,9,9,2,2,9,8,4,1,2,1,5,1,3,3,
%T 6,2,4,6,1,0,4,1,9,5,8,8,1,4,9,0,7,5,9,4,0,9,8,3,1,2,7,8,9,7,7,7,6,6,
%U 6,3,6,5,7,1,9,8,9,0,6,4,1,2,8,3,3,5,2,8,6,2,6,8,1,0,3,5,6,8,5
%N Decimal expansion of Gamma(1/8).
%H G. C. Greubel, <a href="/A203142/b203142.txt">Table of n, a(n) for n = 1..5000</a>
%H Raimundas Vidunas, <a href="http://arxiv.org/abs/math/0403510">Expressions for values of the Gamma function</a>, arXiv:math/0403510 [math.CA], 2004.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Particular_values_of_the_Gamma_function#General_rational_arguments">Particular values of the Gamma function: General rational arguments</a>
%H <a href="/index/Ga#gamma_function">Index to sequences related to the Gamma function</a>
%F this *A203144 * A231863 /2^(1/4) = A068466. - _R. J. Mathar_, Jan 15 2021
%e 7.5339415987976119046992298412151336246104195881490759409831...
%t RealDigits[Gamma[1/8], 10, 100][[1]] (* _Bruno Berselli_, Dec 13 2012 *)
%t RealDigits[Pi^(1/8) * 2^(17/8) * EllipticK[1/2]^(1/4) * EllipticK[3 - 2*Sqrt[2]]^(1/2), 10, 100][[1]] (* _Vaclav Kotesovec_, Apr 15 2024 *)
%o (PARI) default(realprecision, 100); gamma(1/8) \\ _G. C. Greubel_, Jan 15 2017
%o (Magma) SetDefaultRealField(RealField(100)); Gamma(1/8); // _G. C. Greubel_, Mar 10 2018
%K nonn,cons,changed
%O 1,1
%A _N. J. A. Sloane_, Dec 29 2011
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