A388839 - OEIS

%I #12 Jul 13 2026 13:15:20

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

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

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

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

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

%F Empirical: Equals Sum_{k>=0} A246752(k) / exp(k*Pi).

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

%e 0.95305861004894765776518114212209644443...

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

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

%o (PARI) (1/6) * exp(Pi / 3) * Pi * 2^(1/4) * 3^(1/2) * gamma(11/12) * (3^(1/2)-1) / gamma(2/3) / gamma(3/4)^3

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

%Y Cf. A246752.

%K nonn,cons,changed

%O 0,1

%A _Simon Plouffe_, Sep 21 2025