A375370 Decimal expansion of log(2)/3 + zeta(3)/(2*Pi^2).

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

Offset

0,1

Links

Table of n, a(n) for n=0..87.

Olivier Espinosa and Victor H. Moll, On some integrals involving the Hurwitz zeta function: Part 1, Raman. J. 6 (2002) 159-188, eq. (5.7).

Formula

Equals -Integral_{x=0..1} x^2* log(sin(Pi*x)) dx.

Example

0.29194597430343497803291376809503507598583434521003...

Maple

log(2)/3+Zeta(3)/2/Pi^2 ; evalf(%) ;

Mathematica

RealDigits[Log[2] / 3 + Zeta[3] / (2*Pi^2), 10, 120][[1]] (* Amiram Eldar, Aug 19 2024 *)

Prog

(PARI) log(2)/3 + zeta(3)/2/Pi^2 \\ Charles R Greathouse IV, Jul 08 2026

Crossrefs

Cf. A193535.

Sequence in context: A201749 A117033 A152584 * A347292 A388830 A021778

Adjacent sequences: A375367 A375368 A375369 * A375371 A375372 A375373

Keyword

nonn,cons,changed

Author

R. J. Mathar, Aug 13 2024

Status

approved