A388932 Decimal expansion of (4*2^(3/16) * 3^(5/32) * (7+5 * sqrt(2))^(1/8) * exp(Pi / 8) * (Gamma(7/12) * Gamma(11/12))^(5/8) * (Gamma(5/4) * sin(Pi / 8))^(5/4)) / Pi^(5/4).

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

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} A261734(k) / exp(k*Pi).

Equals exp(Pi/8) / (2^(5/16) * (1 + sqrt(2))^(1/4)). - Vaclav Kotesovec, Jan 09 2026

Example

0.95671206149608179533578282572936857320351545435283879994171359346466493728....

Mathematica

First[RealDigits[(4*2^(3/16)*3^(5/32)*(7 + 5*Sqrt[2])^(1/8)*Exp[Pi/8]*(Gamma[7/12]*Gamma[11/12])^(5/8)*(Gamma[5/4]*Sin[Pi/8])^(5/4))/Pi^(5/4), 10, 100]]
RealDigits[E^(Pi/8)/(2^(5/16)*(1 + Sqrt[2])^(1/4)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

Prog

(PARI) exp(Pi / 8) * 3^(5/32) * 2^(13/16) * gamma(5/8)^(5/4) * gamma(11/12)^(5/8) * gamma(7/12)^(5/8) / (2^(1/2) * (2-2^(1/2))^(1/2))^(3/4) / (2^(1/2) * (2+2^(1/2))^(1/2))^(1/2) * (2+2^(1/2))^(1/4) / (2^(1/2) * (1+3^(1/2)))^(5/8) / (2^(1/2) * (3^(1/2)-1))^(5/8) / Pi^(5/8) / gamma(7/8)^(5/4)
(PARI) exp(Pi/8)/(2^(5/16)*(1+sqrt(2))^(1/4)) \\ Charles R Greathouse IV, Jul 14 2026

Crossrefs

Cf. A261734.

Sequence in context: A388668 A388792 A292824 * A388671 A388477 A388624

Adjacent sequences: A388929 A388930 A388931 * A388933 A388934 A388935

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 21 2025

Status

approved