OFFSET
1,5
LINKS
Simon Plouffe, Numbers in the base e^Pi, 2025.
FORMULA
Empirical: Equals Sum_{k>=0} A255318(k) / exp(k*Pi).
Equals exp(11*Pi/24) * Gamma(1/4)^2 / (2^(17/8) * 3^(3/4) * Pi^(3/2)). - Vaclav Kotesovec, Jan 08 2026
EXAMPLE
1.0019517805753381318689637401749890719...
MATHEMATICA
First[RealDigits[(Sqrt[Pi]*Exp[(11*Pi)/24]*Gamma[7/12]^3*Gamma[11/12]^3)/(4*2^(5/8)*Gamma[3/4]^8), 10, 100]]
RealDigits[E^(11*Pi/24) * Gamma[1/4]^2 / (2^(17/8)*3^(3/4)*Pi^(3/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)
PROG
(PARI) (1/8) * exp(11/24 * Pi) * sqrt(Pi) * 2^(3/8) * gamma(11/12)^3 * gamma(7/12)^3 / gamma(3/4)^8
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Simon Plouffe, Sep 21 2025
STATUS
approved
