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A371930 Decimal expansion of Pi^(1/2)*Gamma(1/14)/(7*Gamma(4/7)).

%I A371930 #23 Apr 15 2024 07:14:46
%S A371930 2,1,9,1,4,5,0,2,4,5,2,0,1,0,7,8,5,3,3,9,4,6,2,6,4,8,7,0,3,1,1,7,4,9,
%T A371930 8,8,0,4,3,3,1,0,3,9,5,1,7,8,9,2,5,8,6,7,0,6,5,7,1,1,5,9,4,3,5,3,3,3,
%U A371930 3,3,9,1,0,7,2,1,2,6,0,7,2,7,7,7,2,3,5,1,5,7
%N A371930 Decimal expansion of Pi^(1/2)*Gamma(1/14)/(7*Gamma(4/7)).
%C A371930 Constants from generalized Pi integrals: the case of n=14.
%C A371930 In general, for k > 0, Integral_{x=0..1} 1/sqrt(1 - x^k) dx = 2^(2/k) * Gamma(1 + 1/k)^2 / Gamma(1 + 2/k) = 2^(2/k - 1) * Gamma(1/k)^2 / (k*Gamma(2/k)). - _Vaclav Kotesovec_, Apr 15 2024
%H A371930 Takayuki Tatekawa, <a href="/A371930/b371930.txt">Table of n, a(n) for n = 1..10001</a>
%F A371930 Equals 2*Integral_{x=0..1} dx/sqrt(1-x^14).
%F A371930 Equals Beta(1/14, 1/2) / 7. - _Peter Luschny_, Apr 14 2024
%F A371930 Equals Gamma(1/14)^2 / (7 * 2^(6/7) * Gamma(1/7)). - _Vaclav Kotesovec_, Apr 15 2024
%e A371930 2.191450245201078533946264870311...
%p A371930 Beta(1/14, 1/2) / 7: evalf(%, 90); # _Peter Luschny_, Apr 14 2024
%t A371930 RealDigits[Sqrt[Pi]/7*Gamma[1/14]/Gamma[4/7], 10, 5001][[1]]
%Y A371930 Cf. A085565, A113477, A262427, A371824.
%K A371930 nonn,cons
%O A371930 1,1
%A A371930 _Takayuki Tatekawa_, Apr 12 2024