A256929 Decimal expansion of Sum_{k>=1} (zeta(2*k)/k)*(1/2)^(4*k).

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

Offset: 0

Author

Jean-François Alcover, Apr 13 2015

Keywords

• nonn
• cons
• easy

Examples

			0.1050091150094822100175791691657938595340446113749286903326...
		

References

• H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights, 2011, p. 272, eq. (30).

Links

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

Crossrefs

Cf. A068465, A068467, A093954, A256930.

Programs

Mathematica

RealDigits[Log[Pi/(2*Sqrt[2])], 10, 103] // First

PARI

log(Pi/(2*sqrt(2))) \\ Amiram Eldar, Oct 12 2024

Formula

Equals log(Gamma(3/4)*Gamma(5/4)) = log(A068465*A068467).

Equals log(Pi/(2*sqrt(2))) = log(A093954).

Equals -Sum_{k>=1} log(1 - 1/(4*k)^2). - Amiram Eldar, Aug 12 2020

Extensions

Name corrected by Amiram Eldar, Oct 12 2024