A365959 - OEIS

A365959

Decimal expansion of Sum_{k>=2} zeta(k)/k^2.

8, 3, 5, 9, 9, 8, 3, 3, 2, 7, 0, 0, 9, 6, 4, 3, 2, 2, 9, 7, 0, 9, 1, 1, 1, 9, 8, 6, 9, 6, 0, 2, 9, 0, 9, 6, 4, 2, 7, 0, 4, 2, 1, 6, 8, 0, 9, 3, 2, 3, 3, 2, 4, 8, 3, 2, 9, 5, 5, 6, 3, 4, 9, 2, 5, 7, 7, 0, 1, 8, 9, 5, 2, 5, 3, 1, 7, 3, 8, 8, 4, 0, 0, 2, 1, 9, 2, 2, 7, 6, 8, 8, 7, 7, 6, 6, 2, 2, 3, 2, 5, 7, 7, 8, 5, 5

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..105.

Mathematics Stack Exchange, On a log-gamma definite integral, 2020.

Michael I. Shamos, A catalog of the real numbers, 2011, p. 596.

FORMULA

Equals Sum_{k>=1} (polylog(2, 1/k) - 1/k).

From Velin Yanev, Jul 30 2025: (Start)

Equals Integral_{x=0..1} log(Gamma(1 - x))/x dx - A001620. [Proved by Paul Enta, 2020]

Conjecture: Equals 2 - A001620 - Pi^2/12 + Integral_{x=0..oo} (2*x*arccot(x) - log(1/x^2 + 1))*log(1 - exp(-2*Pi*x))/(2*Pi*(x^2 + 1)) dx. (End)