A396438 Decimal expansion of Sum_{k>=1} (zeta(2*k)/k)*(3/5)^(2*k).

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

Offset

0,1

References

H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights, 2011, p. 272, eq. (34).

Links

Table of n, a(n) for n=0..104.

Formula

Equals log(6*sqrt(2)*Pi/(5*sqrt(5+sqrt(5)))).

Equals log(Gamma(2/5)*Gamma(8/5)).

Example

0.684086052005027982956076086488842223395691645069838...

Mathematica

RealDigits[Log[6*Sqrt[2]*Pi/(5*Sqrt[5+Sqrt[5]])], 10, 120][[1]]

Prog

(PARI) log(6*sqrt(2)*Pi/(5*sqrt(5+sqrt(5))))

Crossrefs

Cf. A094642, A255681, A256921, A256922, A256923, A256929, A256930, A377008, A396436, A396437, A396439, A396440, A396441, A396442, A396443, A396444, A396445.

Sequence in context: A394011 A255728 A272488 * A100608 A350795 A352769

Adjacent sequences: A396435 A396436 A396437 * A396439 A396440 A396441

Keyword

nonn,cons

Author

Amiram Eldar, May 26 2026

Status

approved