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A145438
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Decimal expansion of sum_{n=1..inf} 1/(n^3*binomial(2n,n)).
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5
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5, 2, 2, 9, 4, 6, 1, 9, 2, 1, 3, 3, 3, 3, 5, 1, 0, 8, 4, 9, 1, 1, 8, 5, 1, 8, 3, 5, 2, 7, 3, 0, 3, 5, 4, 0, 1, 6, 3, 0, 4, 4, 5, 9, 1, 7, 4, 3, 9, 7, 7, 8, 4, 1, 4, 6, 5, 9, 4, 1, 0, 1, 4, 1, 4, 4, 2, 0, 7, 3, 5, 7, 7, 6, 4, 4, 1, 3, 2, 9, 9, 3, 1, 5, 0, 4, 2, 6, 2, 1, 9, 1, 3
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OFFSET
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0,1
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COMMENTS
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Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, (1996), 4.1.47 gives Pi*sqrt(3)*(psi(2/3)-psi(1/3))/72-Zeta(3)/3 which is negative and therefore not correct.
Comment from Mikhail Kalmykov (kalmykov.mikhail(AT)googlemail.com), Jun 01 2009: Analytical results for this sum were also given in Eq. (8) of the Kalmykov and Veretin paper. These results confirm the last comment from Alois P. Heinz.
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LINKS
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FORMULA
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Comment from Alois P. Heinz, Feb 08 2009: Maple's answer to this is: a:= sum(1/(n^3*binomial(2*n,n)), n=1..infinity); a:= 1/2 hypergeom([1, 1, 1, 1], [2, 2, 3/2], 1/4); evalf (a, 140); .522946192133335108491185183527303540163044591743977841465941014...
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EXAMPLE
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0.522946...
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MATHEMATICA
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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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