A344965 Decimal expansion of the sum of the reciprocals of the cubes of the zeros of the digamma function (negated).

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, 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, 6, 7, 5, 0, 5, 8, 0, 6, 0, 1, 0, 3, 4, 4, 2, 7, 6, 1, 6

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..87.

István Mező and Michael E. Hoffman, Zeros of the digamma function and its Barnes G-function analogue, Integral Transforms and Special Functions, Vol. 28, No. 11 (2017), pp. 846-858.

Wikipedia, Digamma function.

Formula

Equals -gamma*Pi^2/2 - 4*zeta(3) - gamma^3, where gamma is Euler's constant (A001620).

Example

-7.84898826280450630489883732716055067110164127911638...

Mathematica

RealDigits[EulerGamma*Pi^2/2 + 4*Zeta[3]  + EulerGamma^3, 10, 100][[1]]

Crossrefs

Cf. A344964, A344966, A344967, A344968.

Cf. A001620, A002117, A102753.

Cf. A030169, A175472, A175473, A175474, A256681, A256682, A256683, A256684, A256685, A256686, A256687.

Sequence in context: A292823 A256920 A307065 * A195340 A019794 A020829

Adjacent sequences: A344962 A344963 A344964 * A344966 A344967 A344968

Keyword

nonn,cons

Author

Amiram Eldar, Jun 03 2021

Status

approved