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A240964
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Decimal expansion of Sum_{n>=1} n/sinh(n*Pi).
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4
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0, 9, 4, 5, 7, 3, 0, 1, 9, 6, 6, 4, 7, 6, 1, 9, 3, 9, 5, 1, 3, 5, 8, 8, 9, 0, 0, 8, 5, 4, 4, 1, 3, 8, 4, 9, 3, 1, 4, 9, 5, 5, 3, 2, 9, 3, 1, 9, 2, 2, 4, 0, 1, 0, 4, 9, 7, 9, 5, 1, 5, 3, 1, 9, 5, 5, 5, 9, 2, 1, 0, 2, 7, 5, 4, 7, 6, 6, 3, 1, 1, 2, 8, 9, 7, 7, 4, 0, 1, 4, 8, 4, 9, 0, 9, 9, 6, 5, 1, 5, 2
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OFFSET
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0,2
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COMMENTS
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Prudnikov (p. 721, section 5.3.5, formula 1) has a typo, Gamma(1/4)^4 is correct, not Gamma(1/4)^2. - Vaclav Kotesovec, May 19 2022
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REFERENCES
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A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 1 (Overseas Publishers Association, Amsterdam, 1986).
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LINKS
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FORMULA
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Gamma(1/4)^4/(32*Pi^3) - 1/(4*Pi).
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EXAMPLE
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0.09457301966476193951358890085441384931495532931922401...
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MATHEMATICA
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Join[{0}, RealDigits[Gamma[1/4]^4/(32*Pi^3) - 1/(4*Pi), 10, 100] // First]
N[EllipticK[k]/Pi^2*(EllipticK[k] - EllipticE[k]) /. k -> 1/2, 100] (* Vaclav Kotesovec, May 19 2022 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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