A375369 Decimal expansion of zeta'(2)/(2*Pi^2) + zeta(3)/(4*Pi^2) + log(2*Pi)/12 -gamma/12.

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

Offset

0,2

Comments

zeta'(2)= -0.9375.. is the first derivative of the zeta function, see A073002. gamma is A001620.

Links

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

Olivier Espinosa and Victor H. Moll, On some integrals involving the Hurwitz zeta function: Part 1, Raman. J. 6 (2002) 159-188, Example 6.4.

Formula

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

Example

0.08800682442616658882644178236358001383676326108903...

Maple

Zeta(1, 2)/2/Pi^2+Zeta(3)/4/Pi^2+log(2*Pi)/12-gamma/12 ; evalf(%) ;

Mathematica

RealDigits[Zeta'[2] / (2*Pi^2) + Zeta[3] / (4*Pi^2) + Log[2*Pi] / 12 - EulerGamma / 12, 10, 120, -1][[1]] (* Amiram Eldar, Aug 19 2024 *)

Crossrefs

Cf. A001620, A073002, A375368.

Sequence in context: A291692 A127583 A273818 * A326801 A326802 A179639

Adjacent sequences: A375366 A375367 A375368 * A375370 A375371 A375372

Keyword

nonn,cons,new

Author

R. J. Mathar, Aug 13 2024

Status

approved