A388580 Decimal expansion of (2^(3/4) * sqrt((2-sqrt(2)) / Pi) * exp(Pi / 2) * Gamma(5/4)^2) / Pi.

9, 1, 3, 5, 8, 2, 3, 2, 4, 1, 1, 9, 3, 4, 1, 1, 0, 0, 8, 8, 9, 3, 6, 8, 0, 5, 1, 2, 2, 3, 6, 3, 5, 0, 6, 8, 1, 2, 3, 3, 9, 6, 1, 6, 4, 9, 5, 6, 1, 3, 4, 5, 9, 0, 8, 5, 6, 8, 6, 3, 5, 0, 9, 1, 1, 4, 8, 2, 0, 7, 2, 2, 5, 8, 5, 1, 0, 5, 9, 0, 1, 5, 6, 3, 3, 4, 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} A125095(k) / exp(k*Pi).

Example

0.91358232411934110088936805122363506812...

Mathematica

First[RealDigits[(2^(3/4)*Sqrt[(2 - Sqrt[2])/Pi]*Exp[Pi/2]*Gamma[5/4]^2)/Pi, 10, 100]]

Prog

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

Crossrefs

Cf. A125095.

Sequence in context: A388661 A388480 A248557 * A388660 A388631 A388618

Adjacent sequences: A388577 A388578 A388579 * A388581 A388582 A388583

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 18 2025

Status

approved