A388585 Decimal expansion of (1/8) * exp(Pi/6) * Gamma(2/3) * Gamma(7/12) * sqrt(2) * (1+3^(1/2)) / Gamma(3/4)^3.

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

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} A129451(k) / exp(k*Pi).

Equals sqrt(1 + sqrt(3)) * exp(Pi/6) * Gamma(1/4)^2 / (2^(9/4) * 3^(3/8) * Pi^(3/2)). - Vaclav Kotesovec, Jan 08 2026

Example

0.91714884833813079095696445153820770483...

Mathematica

First[RealDigits[(-16*Sqrt[2 + Sqrt[3]]*Exp[Pi/6]*Gamma[7/12]*Gamma[2/3])/Gamma[-1/4]^3, 10, 100]]
RealDigits[Sqrt[1 + Sqrt[3]] * E^(Pi/6) * Gamma[1/4]^2 / (2^(9/4)*3^(3/8)*Pi^(3/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/8) * exp(1/6 * Pi) * gamma(2/3) * gamma(7/12) * sqrt(2) * (1+3^(1/2)) / gamma(3/4)^3
(PARI) sqrt(1+sqrt(3))*exp(Pi/6)*gamma(1/4)^2/(2^(9/4)*3^(3/8)*Pi^(3/2)) \\ Charles R Greathouse IV, Jul 12 2026

Crossrefs

Cf. A129451.

Sequence in context: A388510 A389045 A021920 * A367960 A280703 A364502

Adjacent sequences: A388582 A388583 A388584 * A388586 A388587 A388588

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 18 2025

Status

approved