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A175571
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Decimal expansion of the Dirichlet beta function of 5.
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14
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9, 9, 6, 1, 5, 7, 8, 2, 8, 0, 7, 7, 0, 8, 8, 0, 6, 4, 0, 0, 6, 3, 1, 9, 3, 6, 8, 6, 3, 0, 9, 7, 5, 2, 8, 1, 5, 1, 1, 3, 9, 5, 5, 2, 9, 3, 8, 8, 2, 6, 4, 9, 4, 3, 2, 0, 7, 9, 8, 3, 2, 1, 5, 1, 2, 4, 4, 6, 2, 8, 6, 5, 0, 1, 8, 2, 7, 4, 8, 1, 9, 2, 8, 9, 6, 5, 9, 8, 3, 2, 2, 7, 0, 5, 2, 4, 4, 7, 5, 5, 9, 9, 0, 8, 0
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OFFSET
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0,1
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COMMENTS
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The value of the Dirichlet L-series L(m=4,r=2,s=4), see arXiv:1008.2547.
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REFERENCES
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L. B. W. Jolley, Summation of Series, Dover, 1961, eq. 308.
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LINKS
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FORMULA
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Equals Product_{p prime >= 3} (1 - (-1)^((p-1)/2)/p^5)^(-1). - Amiram Eldar, Nov 06 2023
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EXAMPLE
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0.99615782807708806400631936...
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MAPLE
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DirichletBeta := proc(s) 4^(-s)*(Zeta(0, s, 1/4)-Zeta(0, s, 3/4)) ; end proc: x := DirichletBeta(5) ; x := evalf(x) ;
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MATHEMATICA
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RealDigits[ DirichletBeta[5], 10, 105] // First (* Jean-François Alcover, Feb 20 2013, updated Mar 14 2018 *)
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PROG
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(PARI) beta(x)=(zetahurwitz(x, 1/4)-zetahurwitz(x, 3/4))/4^x
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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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