A388681 Decimal expansion of ((3+sqrt(3)) * Gamma(7/12)^3 * Gamma(2/3) * Gamma(11/12)^2) / (4*2^(3/4) * Gamma(3/4)^7).

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

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} A164273(k) / exp(k*Pi).

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

Example

0.91372658894753988546447256933279883683708356586979138350013047163801955224....

Mathematica

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

Prog

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

Crossrefs

Cf. A164273.

Sequence in context: A388631 A388618 A388907 * A198819 A176520 A011462

Adjacent sequences: A388678 A388679 A388680 * A388682 A388683 A388684

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 18 2025

Status

approved