A388607 Decimal expansion of (2^(1/4) * (-3+sqrt(3)) * Pi^(5/4) * exp(Pi / 24)) / (Gamma(-1/3) * Gamma(7/12) * Gamma(3/4)^2).

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

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} A133079(k) / exp(k*Pi).

Equals exp(Pi/24) * Gamma(1/4)^3 / (2^(3/2) * 3^(1/8) * sqrt(1 + sqrt(3)) * Pi^(9/4)). - Vaclav Kotesovec, Jan 08 2026

Example

0.77085996361963748482748340415665517736909593348673844492443223015498238333....

Mathematica

First[RealDigits[(2^(1/4)*(-3 + Sqrt[3])*Pi^(5/4)*Exp[Pi/24])/(Gamma[-1/3]*Gamma[7/12]*Gamma[3/4]^2), 10, 100]]
RealDigits[E^(Pi/24)*Gamma[1/4]^3 / (2^(3/2)*3^(1/8)*Sqrt[1 + Sqrt[3]]*Pi^(9/4)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/3) * exp(Pi / 24) * Pi^(5/4) * 2^(1/4) * 3^(1/2) * (3^(1/2)-1) / gamma(2/3) / gamma(3/4)^2 / gamma(7/12)
(PARI) exp(Pi/24) * gamma(1/4)^3 / (2^(3/2) * 3^(1/8) * sqrt(1 + sqrt(3)) * Pi^(9/4)) \\ Charles R Greathouse IV, Jul 11 2026

Crossrefs

Cf. A133079.

Sequence in context: A019725 A064890 A196602 * A200622 A357102 A258149

Adjacent sequences: A388604 A388605 A388606 * A388608 A388609 A388610

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved