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A257871
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Decimal expansion of the Madelung type constant C(2|1/2) (negated).
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3
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6, 9, 1, 3, 0, 3, 9, 5, 7, 7, 0, 0, 9, 1, 6, 1, 1, 0, 7, 8, 5, 0, 1, 8, 7, 8, 1, 4, 2, 6, 9, 7, 7, 9, 1, 2, 3, 0, 2, 1, 0, 0, 8, 9, 5, 0, 6, 9, 1, 5, 9, 4, 3, 2, 7, 1, 3, 9, 7, 9, 8, 3, 2, 9, 8, 2, 7, 1, 8, 9, 0, 5, 2, 7, 2, 9, 5, 2, 7, 5, 9, 6, 8, 2, 3, 2, 9, 4, 6, 9, 1, 1, 5, 5, 7, 3, 2, 7, 1, 9, 6, 1, 1, 2
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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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Equals 2*sqrt(Pi)*zeta(1/2)*(zeta(1/2, 1/4) - zeta(1/2, 3/4)).
Equals 4*Pi^(1 - 2*nu)*gamma(nu)*zeta(nu)*DirichletBeta(nu) with nu = 1/2.
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EXAMPLE
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-6.913039577009161107850187814269779123021008950691594327139798329827...
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MAPLE
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evalf(2*sqrt(Pi)*Zeta(1/2)*(Zeta(0, 1/2, 1/4)-Zeta(0, 1/2, 3/4)), 120); # Vaclav Kotesovec, May 11 2015
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MATHEMATICA
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RealDigits[2*Sqrt[Pi]*Zeta[1/2]*(Zeta[1/2, 1/4] - Zeta[1/2, 3/4]), 10, 104] // First
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PROG
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(PARI) 2*sqrt(Pi)*zeta(1/2)*(zetahurwitz(1/2, 1/4) - zetahurwitz(1/2, 3/4)) \\ Charles R Greathouse IV, Jan 31 2018
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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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