A294967 Decimal expansion of (1/9)*Hurwitz Zeta(2, 2/3) = (1/9)*Psi(1, 2/3), with the Polygamma function Psi.

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

Offset: 0

Author

Wolfdieter Lang, Nov 12 2017

Keywords

• nonn
• cons

Comments

This is the value of the series Sum_{n=0..infinity} 1/(3*n+2)^2. For (3*n+2)^2 see A016790.

For the partial sums see A173986(n+1)/A173987(n+1), n >= 0.

Examples

			0.340430601039857489998590803697298350359188343374823262215864737125448716...
		

Links

• Eric Weisstein's World of Mathematics, Hurwitz Zeta Function.
• Eric Weisstein's World of Mathematics, Polygamma Function.

Crossrefs

Cf. A016790, A173986/A173987, A214550.

Programs

Mathematica

RealDigits[4*Pi^2/27 - PolyGamma[1, 1/3]/9, 10, 126][[1]] (* Amiram Eldar, Oct 02 2020 *)
RealDigits[HurwitzZeta[2, 2/3]/9, 10, 150][[1]] (* Vaclav Kotesovec, Oct 02 2020 *)

PARI

zetahurwitz(2,2/3)/9 \\ Charles R Greathouse IV, Jan 30 2018

Formula

From Amiram Eldar, Oct 02 2020: (Start)

Equals Integral_{1..oo} log(x)/(x^3-1) dx.

Equals 4*Pi^2/27 - A214550. (End)

Extensions

Data corrected by Amiram Eldar, Oct 02 2020