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

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, 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, 8, 8, 2, 0, 4, 9, 0, 5, 3, 5, 9, 2, 9, 1, 1, 6, 2, 1, 4

Offset

1,1

Comments

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.

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 Pi^2/2 + gamma^2, where gamma is Euler's constant (A001620).

Example

5.26798012435239798373562163629331979431626684387002...

Mathematica

RealDigits[Pi^2/2 + EulerGamma^2, 10, 100][[1]]

Crossrefs

Cf. A344965, A344966, A344967, A344968.

Cf. A001620, A102753.

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

Sequence in context: A011506 A054400 A035568 * A321074 A318384 A091660

Adjacent sequences: A344961 A344962 A344963 * A344965 A344966 A344967

Keyword

nonn,cons

Author

Amiram Eldar, Jun 03 2021

Status

approved