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A388939
Decimal expansion of Pi^(1/3) * 3^(2/3) * Gamma(11/12)^(2/3) / Gamma(2/3)^(2/3) / Gamma(3/4)^(2/3) / (sqrt(2) * (1+3^(1/2)))^(2/3).
1
9, 1, 5, 1, 3, 7, 5, 0, 4, 4, 7, 7, 5, 8, 1, 1, 9, 8, 9, 8, 0, 7, 4, 1, 7, 2, 5, 9, 9, 0, 6, 0, 9, 6, 7, 8, 2, 9, 3, 9, 4, 3, 1, 9, 3, 6, 1, 1, 0, 9, 1, 6, 9, 8, 6, 3, 1, 3, 8, 9, 7, 3, 8, 9, 1, 9, 1, 2, 8, 8, 9, 4, 5, 8, 1, 6, 5, 5, 2, 2, 5, 5, 0, 0, 4, 4, 7
OFFSET
0,1
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
Cf. A262930.
Sequence in context: A192930 A010168 A388571 * A393233 A340004 A327963
KEYWORD
nonn,cons
AUTHOR
Simon Plouffe, Sep 21 2025
STATUS
approved