%I #23 Apr 15 2024 07:14:46

%S 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 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 3,3,9,1,0,7,2,1,2,6,0,7,2,7,7,7,2,3,5,1,5,7

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

%C Constants from generalized Pi integrals: the case of n=14.

%C 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 Takayuki Tatekawa, <a href="/A371930/b371930.txt">Table of n, a(n) for n = 1..10001</a>

%F Equals 2*Integral_{x=0..1} dx/sqrt(1-x^14).

%F Equals Beta(1/14, 1/2) / 7. - _Peter Luschny_, Apr 14 2024

%F Equals Gamma(1/14)^2 / (7 * 2^(6/7) * Gamma(1/7)). - _Vaclav Kotesovec_, Apr 15 2024

%e 2.191450245201078533946264870311...

%p Beta(1/14, 1/2) / 7: evalf(%, 90); # _Peter Luschny_, Apr 14 2024

%t RealDigits[Sqrt[Pi]/7*Gamma[1/14]/Gamma[4/7], 10, 5001][[1]]

%Y Cf. A085565, A113477, A262427, A371824.

%K nonn,cons

%O 1,1

%A _Takayuki Tatekawa_, Apr 12 2024