A388807 - OEIS

%I #10 Jul 13 2026 11:40:55

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

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

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

%N Decimal expansion of (1/24) * exp(Pi / 3) * 3^(3/4) * Gamma(2/3) * Gamma(11/12)^2 * Gamma(7/12)^3 * (1+3^(1/2)) / Gamma(3/4)^7.

%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.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F Empirical: Equals Sum_{k>=0} A227696(k) / exp(k*Pi).

%F Equals sqrt(1 + sqrt(3)) * exp(Pi/3) * Gamma(1/4)^2 / (2^(7/4) * 3^(9/8) * Pi^(3/2)). - _Vaclav Kotesovec_, Jan 08 2026

%e 0.96052780421860884567619784916357732122663703782457450209449268497461039434....

%t First[RealDigits[((1 + Sqrt[3])*Exp[Pi/3]*Gamma[7/12]^3*Gamma[2/3]*Gamma[11/12]^2)/(8*3^(1/4)*Gamma[3/4]^7), 10, 100]]

%t RealDigits[Sqrt[1 + Sqrt[3]]*E^(Pi/3)*Gamma[1/4]^2 / (2^(7/4)*3^(9/8)*Pi^(3/2)), 10, 100][[1]] (* _Vaclav Kotesovec_, Jan 08 2026 *)

%o (PARI) (1/24) * exp(Pi / 3) * 3^(3/4) * gamma(2/3) * gamma(11/12)^2 * gamma(7/12)^3 * (1+3^(1/2)) / gamma(3/4)^7

%o (PARI) sqrt(1+sqrt(3))*exp(Pi/3)*gamma(1/4)^2/(2^(7/4)*3^(9/8)*Pi^(3/2)) \\ _Charles R Greathouse IV_, Jul 13 2026

%Y Cf. A227696.

%K nonn,cons,changed

%O 0,1

%A _Simon Plouffe_, Sep 18 2025