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

0,1

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.

Links

Table of n, a(n) for n=0..125.

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

Eric Weisstein's World of Mathematics, Polygamma Function.

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)

Example

0.340430601039857489998590803697298350359188343374823262215864737125448716...

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 *)

Prog

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

Crossrefs

Cf. A016790, A173986/A173987, A214550.

Sequence in context: A110061 A363804 A220956 * A351045 A267183 A021750

Adjacent sequences: A294964 A294965 A294966 * A294968 A294969 A294970

Keyword

nonn,cons

Author

Wolfdieter Lang, Nov 12 2017

Extensions

Data corrected by Amiram Eldar, Oct 02 2020

Status

approved