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A256920
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Decimal expansion of Sum_{k>=1} (-1)^k*(zeta(4k)-1) (negated).
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3
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0, 7, 8, 4, 7, 7, 5, 7, 9, 6, 6, 7, 1, 3, 6, 8, 3, 8, 3, 1, 8, 0, 2, 2, 1, 9, 3, 2, 4, 5, 7, 1, 9, 2, 3, 5, 0, 4, 6, 6, 7, 2, 2, 1, 7, 3, 2, 7, 2, 9, 1, 3, 2, 7, 5, 8, 7, 4, 8, 6, 6, 4, 5, 7, 9, 3, 8, 0, 8, 4, 4, 8, 0, 6, 1, 6, 8, 1, 1, 1, 7, 4, 5, 7, 3, 1, 9, 4, 3, 5, 4, 1, 6, 6, 6, 2, 8, 6, 3, 8, 3, 1, 6, 6, 7, 2
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OFFSET
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0,2
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REFERENCES
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H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights (2011) p. 265.
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LINKS
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FORMULA
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1 + (Pi/(2*Sqrt(2)))*(sin(Pi*sqrt(2)) + sinh(Pi*sqrt(2))) / (cos(Pi*sqrt(2)) - cosh(Pi*sqrt(2))).
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EXAMPLE
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-0.07847757966713683831802219324571923504667221732729...
= 1 - Pi^4/90 + Pi^8/9450 - 691*Pi^12/638512875 + ...
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MATHEMATICA
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Join[{0}, RealDigits[1 + (Pi/(2 Sqrt[2]))*(Sin[Pi*Sqrt[2]] + Sinh[Pi*Sqrt[2]]) / (Cos[Pi*Sqrt[2]] - Cosh[Pi*Sqrt[2]]), 10, 105] // First]
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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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