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Search: id:A131688
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| A131688 |
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Decimal expansion of the constant sum_{k=1..infinity} log(k+1)/k/(k+1). |
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+0
1
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| 1, 2, 5, 7, 7, 4, 6, 8, 8, 6, 9, 4, 4, 3, 6, 9, 6, 3, 0, 0, 0, 9, 8, 9, 9, 8, 3, 0, 4, 9, 5, 8, 8, 1, 5, 2, 8, 5, 1, 1, 5, 4, 0, 8, 9, 0, 5, 0, 8, 8, 8, 4, 8, 6, 8, 9, 7, 7, 5, 4, 0, 8, 3, 3, 5, 2, 2
(list; cons; graph; listen)
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OFFSET
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1,2
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COMMENT
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Equals Sum[ -Zeta'[1 + k], {k, 1, Infinity}], where Zeta' is the derivative of Riemann Zeta function. [From Vladimir Reshetnikov (v.reshetnikov(AT)gmail.com), Dec 28 2008]
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LINKS
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M. W. Coffey, Series of zeta values, the Stieltjes constants and a sum S_gamma(n), arXiv:math-ph/0706.0345, eq (38a).
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FORMULA
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Equals sum_{s=1..infinity} (-1)^(s+1)*zeta(s+1)/s.
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EXAMPLE
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1.257746886944369630009899830495881528511540890508884868977540833522...
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MATHEMATICA
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Sum[ -Zeta'[1 + k], {k, 1, Infinity}] [From Vladimir Reshetnikov (v.reshetnikov(AT)gmail.com), Dec 28 2008]
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PROGRAM
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(PARI) sumalt(s=1, (-1)^(s+1)/s*zeta(s+1) );
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CROSSREFS
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Sequence in context: A078320 A141430 A021392 this_sequence A096624 A145378 A069887
Adjacent sequences: A131685 A131686 A131687 this_sequence A131689 A131690 A131691
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KEYWORD
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cons,nonn
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 14 2007
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