A388624 Decimal expansion of (-6 * (3+sqrt(3)) * exp(-Pi/4) * Gamma(2/3) * Gamma(3/4)) / (sqrt(Pi) * Gamma(-1/12)).

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

Offset

0,1

Links

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

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

Formula

Empirical: Equals Sum_{k>=0} A135211(k) / exp(k*Pi).

Equals 3^(3/8) * sqrt(1 + sqrt(3)) / (exp(Pi/4) * 2^(1/4)). - Vaclav Kotesovec, Jan 08 2026

Example

0.95678260062588529874984470100139184575...

Mathematica

First[RealDigits[(-6*(3 + Sqrt[3])*Exp[-1/4*Pi]*Gamma[2/3]*Gamma[3/4])/(Sqrt[Pi]*Gamma[-1/12]), 10, 100]]
RealDigits[3^(3/8)*Sqrt[1 + Sqrt[3]]/(E^(Pi/4)*2^(1/4)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/2) * exp(-Pi / 4) * 3^(1/2) * gamma(2/3) * gamma(3/4) * (1+3^(1/2)) / gamma(11/12) / sqrt(Pi)

Crossrefs

Cf. A135211.

Sequence in context: A388932 A388671 A388477 * A388891 A388682 A388610

Adjacent sequences: A388621 A388622 A388623 * A388625 A388626 A388627

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved