OFFSET
0,1
LINKS
Simon Plouffe, Numbers in the base e^Pi, 2025.
FORMULA
Empirical: Equals Sum_{k>=0} A262930(k) / exp(k*Pi).
Equals 3^(3/4) / (2^(5/6) * (1 + sqrt(3))^(1/3)). - Vaclav Kotesovec, Jan 09 2026
EXAMPLE
0.91513750447758119898074172599060967829...
MATHEMATICA
First[RealDigits[(Pi/2)^(1/3)*((3*Gamma[11/12])/((1 + Sqrt[3])*Gamma[2/3]*Gamma[3/4]))^(2/3), 10, 100]]
RealDigits[3^(3/4)/(2^(5/6)*(1 + Sqrt[3])^(1/3)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)
PROG
(PARI) Pi^(1/3) * 3^(2/3) * gamma(11/12)^(2/3) / gamma(2/3)^(2/3) / gamma(3/4)^(2/3) / (2^(1/2) * (1+3^(1/2)))^(2/3)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Simon Plouffe, Sep 21 2025
STATUS
approved
