A388451 Decimal expansion of (3/4) * Gamma(2/3)^2 * Gamma(11/12) * Gamma(7/12)^3 * (2+3^(1/2)) * exp(-Pi/3) / Pi / Gamma(3/4)^4.

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

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} A062244(k) / exp(k*Pi).

Equals (1 + sqrt(3)) / exp(Pi/3). - Vaclav Kotesovec, Jan 08 2026

Example

0.95873074259369238706844958821751154768...

Mathematica

First[RealDigits[(3*(2 + Sqrt[3])*Exp[-1/3*Pi]*Gamma[7/12]^3*Gamma[2/3]^2*Gamma[11/12])/(4*Pi*Gamma[3/4]^4), 10, 100]]
RealDigits[(1 + Sqrt[3])/E^(Pi/3), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (3/4) * gamma(2/3)^2 * gamma(11/12) * gamma(7/12)^3 * (2+3^(1/2)) * exp(-1/3 * Pi) / Pi / gamma(3/4)^4
(PARI) (1 + sqrt(3)) / exp(Pi/3) \\ Charles R Greathouse IV, Jul 11 2026

Crossrefs

Cf. A062244.

Sequence in context: A309645 A377227 A351209 * A146483 A090463 A272795

Adjacent sequences: A388448 A388449 A388450 * A388452 A388453 A388454

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 17 2025

Status

approved