A377008 Decimal expansion of Sum_{k>=1} (zeta(2*k)/k)*(2/3)^(2*k).

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

Offset: 0

Author

Amiram Eldar, Oct 12 2024

Keywords

• nonn
• cons
• easy

Examples

			0.88310581396712625588502373888562329082705924490169...
		

References

• H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights, 2011, p. 272, eq. (29).

Links

• Eric Weisstein's MathWorld, Riemann Zeta Function.
• Wikipedia, Riemann zeta function.

Crossrefs

Cf. A073005, A203129, A256923, A275486.

Programs

Mathematica

RealDigits[Log[4*Pi/(3*Sqrt[3])], 10, 120][[1]]
(* or *)
RealDigits[Log[Gamma[1/3]*Gamma[5/3]], 10, 120][[1]]

PARI

log(4*Pi/(3*sqrt(3)))

PARI

log(gamma(1/3)*gamma(5/3))

Formula

Equals log(4*Pi/(3*sqrt(3))) = log(A275486).

Equals log(Gamma(1/3)*Gamma(5/3)).