A388595 Decimal expansion of (sqrt(29+41 / sqrt(2)) * Gamma(5/8)^4) / (8 * Pi * Gamma(7/8)^4).

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

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} A131999(k) / exp(k*Pi).

Equals sqrt(1 + sqrt(2)) * Gamma(1/4)^4 / (2^(13/4) * Pi^3). - Vaclav Kotesovec, Jan 08 2026

Example

0.91015432852376838398807186952497623232...

Mathematica

First[RealDigits[(Sqrt[29 + 41/Sqrt[2]]*Gamma[5/8]^4)/(8*Pi*Gamma[7/8]^4), 10, 100]]
RealDigits[Sqrt[1 + Sqrt[2]]*Gamma[1/4]^4 / (2^(13/4)*Pi^3), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/16) * gamma(5/8)^4 * (3+2 * sqrt(2)) * sqrt(2) * (2+2^(1/2))^(1/2) / Pi / gamma(7/8)^4

Crossrefs

Cf. A131999.

Sequence in context: A257097 A256667 A175764 * A388388 A388816 A388468

Adjacent sequences: A388592 A388593 A388594 * A388596 A388597 A388598

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved