%I #8 Sep 25 2025 18:28:30

%S 1,0,9,8,6,5,3,4,6,1,8,8,7,3,2,9,5,7,2,7,9,4,2,3,5,1,7,5,2,3,5,4,7,9,

%T 2,5,8,3,5,5,2,4,1,0,2,2,5,8,0,5,2,3,2,2,6,2,5,1,5,6,8,0,1,7,8,7,4,3,

%U 4,4,9,9,0,6,3,1,4,8,8,8,8,2,6,5,1,2,5

%N Decimal expansion of (8 * sqrt(20+14 * sqrt(2)) * Gamma(5/4)^4) / Pi^3.

%H Simon Plouffe, <a href="https://plouffe.fr/articles/numbers%20in%20the%20base_exp_english%202025.pdf">Numbers in the base e^Pi</a>, 2025.

%F Empirical: Equals Sum_{k>=0} A320149(k) / exp(k*Pi).

%e 1.0986534618873295727942351752354792584...

%t First[RealDigits[(8*Sqrt[20 + 14*Sqrt[2]]*Gamma[5/4]^4)/Pi^3, 10, 100]]

%o (PARI) -(1/16) * gamma(5/8)^4 * (3+2 * sqrt(2)) * (2+2^(1/2))^(1/2) / Pi / gamma(7/8)^4 / (2^(1/2)-2)

%Y Cf. A320149.

%K nonn,cons

%O 1,3

%A _Simon Plouffe_, Sep 22 2025