A388807 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.

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

Offset

0,1

Links

Table of n, a(n) for n=0..86.

Simon Plouffe, Numbers in the base e^Pi, 2025.

Index entries for transcendental numbers.

Formula

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

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

Example

0.96052780421860884567619784916357732122663703782457450209449268497461039434....

Mathematica

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]]
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 *)

Prog

(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
(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

Crossrefs

Cf. A227696.

Sequence in context: A380737 A393636 A336001 * A361601 A130590 A388910

Adjacent sequences: A388804 A388805 A388806 * A388808 A388809 A388810

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 18 2025

Status

approved