A388398 Decimal expansion of (sqrt(3 * (2+sqrt(3))) * Pi^(1/4) * Gamma(7/12)^3 * Gamma(2/3) * Gamma(11/12)^2) / (4 * Gamma(3/4)^8).

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

Offset

1,3

Links

Table of n, a(n) for n=1..87.

Simon Plouffe, Numbers in the base e^Pi, 2025.

Index entries for transcendental numbers.

Formula

Empirical: Equals Sum_{k>=0} A034933(k) / exp(k*Pi).

Equals sqrt(1 + sqrt(3)) * Gamma(1/4)^3 / (2^(7/4) * 3^(3/8) * Pi^(9/4)). - Vaclav Kotesovec, Jan 08 2026

Example

1.1805311048499148127913065372542809959...

Mathematica

First[RealDigits[(Sqrt[3*(2 + Sqrt[3])]*Pi^(1/4)*Gamma[7/12]^3*Gamma[2/3]*Gamma[11/12]^2)/(4*Gamma[3/4]^8), 10, 100]]
RealDigits[Sqrt[1 + Sqrt[3]] * Gamma[1/4]^3 / (2^(7/4) * 3^(3/8) * Pi^(9/4)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/8) * Pi^(1/4) * 3^(1/2) * gamma(2/3) * gamma(11/12)^2 * gamma(7/12)^3 * sqrt(2) * (1+3^(1/2)) / gamma(3/4)^8
(PARI) sqrt(1 + sqrt(3)) * Gamma(1/4)^3 / (2^(7/4) * 3^(3/8) * Pi^(9/4)) \\ Charles R Greathouse IV, Jul 11 2026

Crossrefs

Cf. A034933.

Sequence in context: A393355 A021558 A335958 * A389051 A395468 A308739

Adjacent sequences: A388395 A388396 A388397 * A388399 A388400 A388401

Keyword

nonn,cons

Author

Simon Plouffe, Sep 15 2025

Status

approved