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.

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, 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, 9, 4, 4, 8, 1, 5, 8, 4, 3, 3, 7, 3, 7, 2, 1, 2, 3, 7, 4

Offset

1,1

Comments

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.

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/(6*gamma) + gamma, where gamma is Euler's constant (A001620).

Example

3.42698944421993633539867188882667127331063787917025...

Mathematica

RealDigits[Pi^2/(6*EulerGamma) + EulerGamma, 10, 100][[1]]

Crossrefs

Cf. A344964, A344965, A344966, A344967.

Cf. A001620, A013661.

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

Sequence in context: A297104 A243256 A269868 * A324340 A046692 A205769

Adjacent sequences: A344965 A344966 A344967 * A344969 A344970 A344971

Keyword

nonn,cons

Author

Amiram Eldar, Jun 03 2021

Status

approved