A345385 Decimal expansion of Sum_{k>=2} zeta''(k).
2, 3, 3, 6, 3, 1, 3, 1, 7, 6, 0, 5, 8, 9, 3, 3, 2, 9, 1, 9, 9, 6, 5, 1, 5, 4, 8, 1, 3, 7, 7, 7, 1, 2, 2, 4, 4, 7, 5, 5, 7, 6, 9, 7, 9, 4, 3, 3, 0, 2, 7, 0, 7, 9, 6, 7, 7, 6, 7, 8, 2, 7, 0, 8, 7, 8, 2, 9, 2, 8, 9, 1, 6, 3, 6, 9, 0, 1, 4, 0, 0, 2, 7, 2, 1, 3, 5, 9, 7, 4, 0, 7, 0, 6, 0, 8, 3, 1, 4, 7, 9, 3, 6, 2, 2
Offset: 1
Examples
2.3363131760589332919965154813777122447557697943302707967767827087829289...
Links
- Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 538.
- Michael I. Shamos, A catalog of the real numbers 2011, p. 355.
Programs
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Maple
evalf(Sum(Zeta(2, k), k = 2..infinity), 120);
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Mathematica
RealDigits[Sum[Zeta''[k], {k, 2, 1000}], 10, 110][[1]] -
PARI
suminf(k=2, zeta''(k))
Formula
Equals Sum_{k>=1} log(k+1)^2 / (k*(k+1)).