A388797 Decimal expansion of ((3+sqrt(3)) * exp(Pi / 24) * Gamma(7/12)^3 * Gamma(2/3) * Gamma(11/12)^2) / (4*2^(7/8) * Gamma(3/4)^7).

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

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} A226289(k) / exp(k*Pi).

Equals sqrt(1 + sqrt(3)) * exp(Pi/24) * Gamma(1/4)^2 / (2^(13/8) * 3^(3/8) * Pi^(3/2)). - Vaclav Kotesovec, Jan 08 2026

Example

0.95507291295901583337824517401324570346...

Mathematica

First[RealDigits[((3 + Sqrt[3])*Exp[Pi/24]*Gamma[7/12]^3*Gamma[2/3]*Gamma[11/12]^2)/(4*2^(7/8)*Gamma[3/4]^7), 10, 100]]
RealDigits[Sqrt[1 + Sqrt[3]] * E^(Pi/24) * Gamma[1/4]^2 / (2^(13/8)*3^(3/8)*Pi^(3/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/8) * exp(Pi / 24) * 2^(1/8) * 3^(1/2) * gamma(2/3) * gamma(11/12)^2 * gamma(7/12)^3 * (1+3^(1/2)) / gamma(3/4)^7

Crossrefs

Cf. A226289.

Sequence in context: A199792 A193960 A377522 * A195696 A362000 A197838

Adjacent sequences: A388794 A388795 A388796 * A388798 A388799 A388800

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved