A388871 Decimal expansion of (1/8) * 3^(7/12) * sqrt(2) * Gamma(2/3)^(8/3) * Gamma(11/12)^(4/3) * Gamma(7/12)^4 * (7+4*3^(1/2)) / (sqrt(2) * (1+3^(1/2)))^(4/3) / Pi^(7/12) / Gamma(3/4)^(25/3).

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

Offset

0,1

Links

Table of n, a(n) for n=0..86.

Simon Plouffe, Numbers in the base e^Pi, 2025.

Formula

Empirical: Equals Sum_{k>=0} A246927(k) / exp(k*Pi).

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

Example

0.95709146689392245662861933645967858700...

Mathematica

First[RealDigits[((7 + 4*Sqrt[3])*(3/Pi)^(7/12)*Gamma[7/12]^4*Gamma[2/3]^(8/3)*Gamma[11/12]^(4/3))/(8*2^(1/6)*(1 + Sqrt[3])^(4/3)*Gamma[3/4]^(25/3)), 10, 100]]
RealDigits[(1 + Sqrt[3])^(4/3)*Gamma[1/4]^3/(2^(8/3)*3^(3/4)*Pi^(9/4)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/8) * 3^(7/12) * sqrt(2) * gamma(2/3)^(8/3) * gamma(11/12)^(4/3) * gamma(7/12)^4 * (7+4*3^(1/2)) / (2^(1/2) * (1+3^(1/2)))^(4/3) / Pi^(7/12) / gamma(3/4)^(25/3)

Crossrefs

Cf. A246927.

Sequence in context: A011259 A376330 A393960 * A377616 A155754 A273840

Adjacent sequences: A388868 A388869 A388870 * A388872 A388873 A388874

Keyword

nonn,cons

Author

Simon Plouffe, Sep 21 2025

Status

approved