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Decimal expansion of Sum_{k>=1} log(k+1/2)/k^2 .
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%I #8 May 04 2021 07:59:35

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

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

%N Decimal expansion of Sum_{k>=1} log(k+1/2)/k^2 .

%F Sum_{k >=1 } log(k+eps)/k^2 = -Zeta'(2) - Sum_{i=1} (-eps)^i *Zeta(i+2)/i at eps=1/2, weighted sum over Riemann-Zeta.

%e 1.435062...

%o (PARI) sumpos(k=1, log(k+1/2)/k^2) \\ _Michel Marcus_, May 04 2021

%Y Cf. A073002 (eps=0).

%K nonn,cons

%O 1,2

%A _R. J. Mathar_, May 04 2021