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A344964 Decimal expansion of the sum of the reciprocals of the squares of the zeros of the digamma function.

%I A344964 #13 Jul 24 2025 13:45:42
%S A344964 5,2,6,7,9,8,0,1,2,4,3,5,2,3,9,7,9,8,3,7,3,5,6,2,1,6,3,6,2,9,3,3,1,9,
%T A344964 7,9,4,3,1,6,2,6,6,8,4,3,8,7,0,0,2,5,0,5,6,3,5,7,5,0,8,0,2,6,1,1,2,2,
%U A344964 8,8,2,0,4,9,0,5,3,5,9,2,9,1,1,6,2,1,4
%N A344964 Decimal expansion of the sum of the reciprocals of the squares of the zeros of the digamma function.
%C A344964 The sum is Sum_{k>=0} 1/x_k^2, where x_k is the k-th zero of the digamma function, i.e., root of psi(x) = 0: x_0 = 1.461632... (A030169) is the only positive root, x_1 = -0.504083... (A175472), etc.
%H A344964 István Mező and Michael E. Hoffman, <a href="https://doi.org/10.1080/10652469.2017.1376193">Zeros of the digamma function and its Barnes G-function analogue</a>, Integral Transforms and Special Functions, Vol. 28, No. 11 (2017), pp. 846-858.
%H A344964 Wikipedia, <a href="https://en.wikipedia.org/wiki/Digamma_function">Digamma function</a>.
%F A344964 Equals Pi^2/2 + gamma^2 = A102753 + A155969, where gamma is Euler's constant (A001620).
%e A344964 5.26798012435239798373562163629331979431626684387002...
%t A344964 RealDigits[Pi^2/2 + EulerGamma^2, 10, 100][[1]]
%Y A344964 Cf. A344965, A344966, A344967, A344968.
%Y A344964 Cf. A001620, A102753.
%Y A344964 Cf. A030169, A175472, A175473, A175474, A256681, A256682, A256683, A256684, A256685, A256686, A256687.
%K A344964 nonn,cons
%O A344964 1,1
%A A344964 _Amiram Eldar_, Jun 03 2021