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A294967 Decimal expansion of (1/9)*Hurwitz Zeta(2, 2/3) = (1/9)*Psi(1, 2/3), with the Polygamma function Psi. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
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: A139401 A110061 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

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Last modified May 23 17:47 EDT 2022. Contains 353993 sequences. (Running on oeis4.)