A256923 Decimal expansion of Sum_{k>=1} (zeta(2k)/k)*(1/3)^(2k).

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

Offset: 0

Author

Jean-François Alcover, Apr 13 2015

Keywords

• nonn
• cons
• easy

Examples

			0.189958633407180946467791617427446722751559110541442648...
		

References

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

Links

• Eric Weisstein's MathWorld, Riemann Zeta Function
• Wikipedia, Riemann Zeta Function

Crossrefs

Cf. A073006, A202623, A248897, A256924.

Programs

Mathematica

RealDigits[Log[2*Pi/(3*Sqrt[3])], 10, 105] // First

Formula

Equals log(Gamma(2/3)*Gamma(4/3)).

Equals log(2*Pi/(3*sqrt(3))).

Equals log(A248897).

Equals -Sum_{k>=1} log(1 - 1/(3*k)^2). - Amiram Eldar, Aug 12 2020