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A294967
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Decimal expansion of (1/9)*Hurwitz Zeta(2, 2/3) = (1/9)*Psi(1, 2/3), with the Polygamma function Psi.
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3
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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
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OFFSET
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0,1
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COMMENTS
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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.
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LINKS
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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.
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FORMULA
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From Amiram Eldar, Oct 02 2020: (Start)
Equals Integral_{1..oo} log(x)/(x^3-1) dx.
Equals 4*Pi^2/27 - A214550. (End)
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EXAMPLE
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0.340430601039857489998590803697298350359188343374823262215864737125448716...
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MATHEMATICA
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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 *)
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PROG
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(PARI) zetahurwitz(2, 2/3)/9 \\ Charles R Greathouse IV, Jan 30 2018
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CROSSREFS
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Cf. A016790, A173986/A173987, A214550.
Sequence in context: A139401 A110061 A220956 * A351045 A267183 A021750
Adjacent sequences: A294964 A294965 A294966 * A294968 A294969 A294970
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KEYWORD
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nonn,cons
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AUTHOR
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Wolfdieter Lang, Nov 12 2017
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EXTENSIONS
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Data corrected by Amiram Eldar, Oct 02 2020
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STATUS
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approved
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