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A255701
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Decimal expansion of the Plouffe sum S(5,1) = Sum_{n >= 1} 1/(n^5*(exp(Pi*n)-1)).
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8
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4, 5, 2, 2, 4, 5, 0, 7, 7, 1, 0, 6, 7, 3, 4, 3, 0, 5, 6, 0, 8, 5, 1, 1, 4, 9, 5, 5, 1, 7, 0, 5, 5, 5, 7, 1, 4, 5, 3, 3, 1, 6, 3, 2, 1, 9, 5, 0, 1, 4, 7, 2, 0, 1, 9, 2, 1, 0, 6, 0, 1, 7, 6, 5, 6, 5, 6, 3, 9, 5, 0, 6, 8, 5, 1, 8, 4, 2, 8, 3, 5, 6, 0, 2, 8, 6, 6, 4, 8, 1, 4, 3, 6, 3, 4, 9, 1, 8, 9, 4, 9, 5, 8, 8
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OFFSET
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-1,1
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LINKS
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FORMULA
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This is the case k=5, m=1 of S(k,m) = Sum_{n >= 1} 1/(n^k*(exp(m*Pi*n)-1)).
zeta(5) = 24*S(5,1) - (259/10)*S(5,2) - (1/10)*S(5,4).
Equals Sum_{k>=1} sigma_5(k)/(k^5*exp(Pi*k)). - Amiram Eldar, Jun 05 2023
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EXAMPLE
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0.0452245077106734305608511495517055571453316321950147201921...
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MATHEMATICA
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digits = 104; S[5, 1] = NSum[1/(n^5*(Exp[Pi*n] - 1)), {n, 1, Infinity}, WorkingPrecision -> digits+10, NSumTerms -> digits]; RealDigits[S[5, 1], 10, digits] // First
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CROSSREFS
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Cf. A255695 (S(1,1)), A084254 (S(1,2)), A255697 (S(1,4)), A255698 (S(3,1)), A255699 (S(3,2)), A255700 (S(3,4)), A255702 (S(5,2)), A255703 (S(5,4)).
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KEYWORD
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AUTHOR
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STATUS
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approved
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