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A319461
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Decimal expansion of Pi^2/8 - (3/8)*log(2)^2.
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1
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1, 0, 5, 3, 5, 3, 0, 6, 6, 9, 9, 1, 6, 8, 4, 4, 2, 9, 3, 1, 0, 4, 1, 4, 7, 9, 2, 7, 6, 1, 2, 0, 1, 9, 5, 2, 7, 5, 1, 5, 2, 5, 5, 0, 6, 9, 0, 5, 7, 1, 4, 4, 2, 3, 3, 2, 2, 6, 5, 9, 4, 6, 2, 1, 9, 1, 8, 6, 3, 1, 0, 8, 4, 4, 5, 4, 9, 6, 2, 7, 2, 8, 3, 0, 0, 2, 4, 1
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OFFSET
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1,3
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COMMENTS
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Ramanujan's question 642, part 2, in the Journal of the Indian Mathematical Society (VII, 80) asked: "Show that Sum_{n>=0} (Sum_{k=0..n} 1/(2*k + 1)) * 9^(-n)/(2*n + 1) = Pi^2/8 - (3/8)*log(2)^2".
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LINKS
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EXAMPLE
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1.0535306699168442931041479276120195275152550690571442332...
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MATHEMATICA
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RealDigits[Pi^2/8 - 3*Log[2]^2/8, 10, 120][[1]] (* Amiram Eldar, Jun 27 2023 *)
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PROG
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(PARI) Pi^2/8-(3/8)*log(2)^2
(PARI) suminf(n=0, sum(k=0, n, 1/(2*k+1))*9^(-n)/(2*n+1))
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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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