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%I #12 Jun 04 2021 04:40:12
%S 7,8,4,8,9,8,8,2,6,2,8,0,4,5,0,6,3,0,4,8,9,8,8,3,7,3,2,7,1,6,0,5,5,0,
%T 6,7,1,1,0,1,6,4,1,2,7,9,1,1,6,3,8,0,3,2,9,2,3,2,5,3,0,0,3,4,9,8,6,4,
%U 6,7,5,0,5,8,0,6,0,1,0,3,4,4,2,7,6,1,6
%N Decimal expansion of the sum of the reciprocals of the cubes of the zeros of the digamma function (negated).
%C The sum is Sum_{k>=0} 1/x_k^3, 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 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Digamma_function">Digamma function</a>.
%F Equals -gamma*Pi^2/2 - 4*zeta(3) - gamma^3, where gamma is Euler's constant (A001620).
%e -7.84898826280450630489883732716055067110164127911638...
%t RealDigits[EulerGamma*Pi^2/2 + 4*Zeta[3] + EulerGamma^3, 10, 100][[1]]
%Y Cf. A344964, A344966, A344967, A344968.
%Y Cf. A001620, A002117, A102753.
%Y Cf. A030169, A175472, A175473, A175474, A256681, A256682, A256683, A256684, A256685, A256686, A256687.
%K nonn,cons
%O 1,1
%A _Amiram Eldar_, Jun 03 2021
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