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A344966 Decimal expansion of the sum of the reciprocals of the fourth powers of the zeros of the digamma function.

%I A344966 #11 Jun 04 2021 04:40:19
%S A344966 1,5,9,0,1,8,4,7,0,3,3,2,2,3,4,9,1,5,6,9,7,2,0,8,4,5,5,7,3,5,8,4,2,5,
%T A344966 1,7,6,5,1,9,2,5,6,6,7,2,6,4,3,4,0,2,0,4,1,0,5,7,5,7,1,6,7,9,6,5,2,1,
%U A344966 0,5,3,8,3,8,8,6,4,6,8,5,7,8,8,9,3,2,4
%N A344966 Decimal expansion of the sum of the reciprocals of the fourth powers of the zeros of the digamma function.
%C A344966 The sum is Sum_{k>=0} 1/x_k^4, 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 A344966 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 A344966 Wikipedia, <a href="https://en.wikipedia.org/wiki/Digamma_function">Digamma function</a>.
%F A344966 Equals Pi^4/9 + 2*gamma^2*Pi^2/3 + 4*gamma*zeta(3) + gamma^4, where gamma is Euler's constant (A001620).
%e A344966 15.90184703322349156972084557358425176519256672643402...
%t A344966 RealDigits[Pi^4/9 + 2*EulerGamma^2*Pi^2/3 + 4*EulerGamma*Zeta[3] + EulerGamma^4, 10, 100][[1]]
%Y A344966 Cf. A344964, A344965, A344967, A344968.
%Y A344966 Cf. A000796, A001620, A002117.
%Y A344966 Cf. A030169, A175472, A175473, A175474, A256681, A256682, A256683, A256684, A256685, A256686, A256687.
%K A344966 nonn,cons
%O A344966 2,2
%A A344966 _Amiram Eldar_, Jun 03 2021