A388929 - OEIS

%I #8 Jan 09 2026 03:24:02

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

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

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

%N Decimal expansion of Pi^(5/4) * 3^(1/4) * Gamma(11/12) * (3^(1/2)-1) / Gamma(2/3) / Gamma(3/4)^4.

%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} A261394(k) / exp(k*Pi).

%F Equals 3^(3/8) * Gamma(1/4)^3 / (2^(5/4) * sqrt(1 + sqrt(3)) * Pi^(9/4)). - _Vaclav Kotesovec_, Jan 09 2026

%e 1.3929791042022874617110949187750262205...

%t First[RealDigits[(3^(1/4)*(-1 + Sqrt[3])*Pi^(5/4)*Gamma[11/12])/(Gamma[2/3]*Gamma[3/4]^4), 10, 100]]

%t RealDigits[3^(3/8)*Gamma[1/4]^3 / (2^(5/4)*Sqrt[1 + Sqrt[3]]*Pi^(9/4)), 10, 100][[1]] (* _Vaclav Kotesovec_, Jan 09 2026 *)

%o (PARI) Pi^(5/4) * 3^(1/4) * gamma(11/12) * (3^(1/2)-1) / gamma(2/3) / gamma(3/4)^4

%Y Cf. A261394.

%K nonn,cons

%O 1,2

%A _Simon Plouffe_, Sep 21 2025