A388558 - OEIS

%I #12 Jul 12 2026 14:45:15

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

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

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

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

%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} A113660(k) / exp(k*Pi).

%F Equals 3^(3/8) * sqrt(sqrt(3) - 1) * Gamma(1/4)^2 / (2^(5/4) * Pi^(3/2)). - _Vaclav Kotesovec_, Jan 08 2026

%e 1.28215617708957346102622312303914894886906787429572117609770761745743608870....

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

%t RealDigits[3^(3/8)*Sqrt[Sqrt[3] - 1]*Gamma[1/4]^2 / (2^(5/4)*Pi^(3/2)), 10, 100][[1]] (* _Vaclav Kotesovec_, Jan 08 2026 *)

%o (PARI) (2/3) * Pi * 3^(1/2) * sqrt(2) * (3^(1/2)-1) * gamma(3/4)^3 / gamma(11/12)^2 / gamma(7/12)^3 / gamma(2/3)

%o (PARI) 3^(3/8)*sqrt(sqrt(3)-1)*gamma(1/4)^2/(2^(5/4)*Pi^(3/2)) \\ _Charles R Greathouse IV_, Jul 12 2026

%Y Cf. A113660.

%K nonn,cons,changed

%O 1,2

%A _Simon Plouffe_, Sep 18 2025