A388924 Decimal expansion of (1/4) * Gamma(2/3)^2 * Gamma(7/12)^2 * (2+3^(1/2)) / Pi / Gamma(3/4)^2.

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

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} A261320(k) / exp(k*Pi).

Equals (1 + sqrt(3)) / (sqrt(2) * 3^(3/4)). - Vaclav Kotesovec, Jan 09 2026

Example

0.84748658561247082609040866068070998448...

Mathematica

First[RealDigits[(4*(2 + Sqrt[3])*Gamma[7/12]^2*Gamma[2/3]^2)/(Pi*Gamma[-1/4]^2), 10, 100]]
RealDigits[(1 + Sqrt[3])/(Sqrt[2]*3^(3/4)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

Prog

(PARI) (1/4) * gamma(2/3)^2 * gamma(7/12)^2 * (2+3^(1/2)) / Pi / gamma(3/4)^2

Crossrefs

Cf. A261320.

Sequence in context: A249415 A021122 A395407 * A388239 A389048 A110233

Adjacent sequences: A388921 A388922 A388923 * A388925 A388926 A388927

Keyword

nonn,cons

Author

Simon Plouffe, Sep 21 2025

Status

approved