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A152419
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Decimal expansion of 3-Pi^2/6-zeta(3).
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1
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1, 5, 3, 0, 0, 9, 0, 2, 9, 9, 9, 2, 1, 7, 9, 2, 7, 8, 1, 2, 7, 8, 4, 6, 6, 7, 1, 8, 4, 2, 5, 2, 4, 8, 2, 0, 0, 1, 6, 0, 6, 3, 8, 0, 6, 4, 5, 2, 7, 0, 2, 6, 8, 0, 4, 7, 2, 1, 7, 0, 2, 1, 5, 2, 8, 8, 1, 5, 4, 3, 2, 3, 8, 1, 0, 4, 8, 6, 0, 3, 5, 9, 7, 9, 9, 1, 5, 2, 2, 5, 7, 7, 0, 9, 0, 6, 0, 3, 6, 5, 4, 9, 7, 9, 6
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OFFSET
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0,2
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COMMENTS
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Consider the constants N(s) = Sum_{n>=2} 1/(n^s*(n-1)) = s-Sum_{k=2..s} zeta(k), where zeta() is Riemann's zeta function. We have N(1)=1 and this constant here is N(3).
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LINKS
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FORMULA
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EXAMPLE
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0.15300902999217927812784667184252482001606380645270268047217021528815...
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MAPLE
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evalf(3-Pi^2/6-Zeta(3));
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MATHEMATICA
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RealDigits[3-Pi^2/6-Zeta[3], 10, 120][[1]] (* Harvey P. Dale, Jul 01 2022 *)
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PROG
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(Sage) t(n) = 1/(n*(n+1)^(3));
sum(t(n), n, 1, oo).n(digits=107); # Jani Melik, Nov 20 2020
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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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