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A344968 Decimal expansion of Sum_{k>=0} 1/(x_k^2 - x_k), where x_k is the k-th zero of the digamma function.

%I A344968 #9 Jun 04 2021 04:40:33
%S A344968 3,4,2,6,9,8,9,4,4,4,2,1,9,9,3,6,3,3,5,3,9,8,6,7,1,8,8,8,8,2,6,6,7,1,
%T A344968 2,7,3,3,1,0,6,3,7,8,7,9,1,7,0,2,5,9,0,1,1,8,9,1,7,7,4,0,3,3,1,6,2,0,
%U A344968 9,4,4,8,1,5,8,4,3,3,7,3,7,2,1,2,3,7,4
%N A344968 Decimal expansion of Sum_{k>=0} 1/(x_k^2 - x_k), where x_k is the k-th zero of the digamma function.
%C A344968 The zeros of the digamma function, i.e., the roots of psi(x) = 0 are x_0 = 1.461632... (A030169), the only positive root, x_1 = -0.504083... (A175472), etc.
%H A344968 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 A344968 Wikipedia, <a href="https://en.wikipedia.org/wiki/Digamma_function">Digamma function</a>.
%F A344968 Equals Pi^2/(6*gamma) + gamma, where gamma is Euler's constant (A001620).
%e A344968 3.42698944421993633539867188882667127331063787917025...
%t A344968 RealDigits[Pi^2/(6*EulerGamma) + EulerGamma, 10, 100][[1]]
%Y A344968 Cf. A344964, A344965, A344966, A344967.
%Y A344968 Cf. A001620, A013661.
%Y A344968 Cf. A030169, A175472, A175473, A175474, A256681, A256682, A256683, A256684, A256685, A256686, A256687.
%K A344968 nonn,cons
%O A344968 1,1
%A A344968 _Amiram Eldar_, Jun 03 2021