A388584 Decimal expansion of (sqrt((-1+sqrt(3)) * Pi) * exp((11 * Pi) / 24) * (Gamma(7/12) * Gamma(11/12))^(3/2)) / (4*2^(1/8) * Gamma(3/4)^5).

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

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} A128591(k) / exp(k*Pi).

Equals exp(11*Pi/24) * sqrt(sqrt(3) - 1) * Gamma(1/4)^2 / (2^(19/8) * 3^(3/8) * Pi^(3/2)). - Vaclav Kotesovec, Jan 08 2026

Example

1.08837963015203197620154376691690408686331539351004440436992547358588833461....

Mathematica

First[RealDigits[(Sqrt[(-1 + Sqrt[3])*Pi]*Exp[(11*Pi)/24]*(Gamma[7/12]*Gamma[11/12])^(3/2))/(4*2^(1/8)*Gamma[3/4]^5), 10, 100]]
RealDigits[E^(11*Pi/24)*Sqrt[Sqrt[3] - 1] * Gamma[1/4]^2 / (2^(19/8)*3^(3/8)*Pi^(3/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/4) * exp(11/24 * Pi) * sqrt(Pi) * 2^(1/8) * gamma(11/12)^(3/2) * gamma(7/12)^(3/2) * (3^(1/2)-1) / gamma(3/4)^5 / (2^(1/2) * (3^(1/2)-1))^(1/2)
(PARI) exp(11*Pi/24)*sqrt(sqrt(3)-1)*gamma(1/4)^2/(2^(19/8)*3^(3/8)*Pi^(3/2)) \\ Charles R Greathouse IV, Jul 12 2026

Crossrefs

Cf. A128591.

Sequence in context: A254291 A219300 A200686 * A389400 A222066 A388938

Adjacent sequences: A388581 A388582 A388583 * A388585 A388586 A388587

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 18 2025

Status

approved