A388648 Decimal expansion of (1/2) * exp(-Pi/8) * 2^(1/8) * Gamma(2/3) * Gamma(7/12) * (1+3^(1/2)) / Gamma(3/4) / sqrt(Pi).

9, 5, 8, 6, 5, 6, 7, 1, 6, 6, 6, 0, 6, 1, 3, 2, 2, 9, 5, 1, 9, 9, 3, 3, 7, 3, 0, 0, 6, 8, 7, 4, 9, 8, 0, 5, 4, 8, 8, 1, 8, 4, 5, 8, 5, 2, 2, 7, 3, 3, 6, 6, 6, 0, 9, 0, 9, 1, 7, 8, 7, 5, 7, 4, 3, 7, 1, 7, 0, 8, 1, 3, 2, 8, 7, 1, 7, 1, 4, 2, 1, 3, 6, 4, 1, 7, 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} A143066(k) / exp(k*Pi).

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

Example

0.95865671666061322951993373006874980548...

Mathematica

First[RealDigits[((1 + Sqrt[3])*Exp[-1/8*Pi]*Gamma[7/12]*Gamma[2/3])/(2^(7/8)*Sqrt[Pi]*Gamma[3/4]), 10, 100]]
RealDigits[(2/3)^(3/8)*Sqrt[1 + Sqrt[3]] / E^(Pi/8), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/2) * exp(-1/8 * Pi) * 2^(1/8) * gamma(2/3) * gamma(7/12) * (1+3^(1/2)) / gamma(3/4) / sqrt(Pi)

Crossrefs

Cf. A143066.

Sequence in context: A388897 A388805 A388614 * A309645 A377227 A351209

Adjacent sequences: A388645 A388646 A388647 * A388649 A388650 A388651

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved