A256681 -id:A256681 - cp's OEIS frontend

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

Amiram Eldar, Jun 03 2021

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.

			3.42698944421993633539867188882667127331063787917025...

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.

Cf. A344964, A344965, A344966, A344967.
Cf. A001620, A013661.
Cf. A030169, A175472, A175473, A175474, A256681, A256682, A256683, A256684, A256685, A256686, A256687.

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

Equals Pi^2/(6*gamma) + gamma, where gamma is Euler's constant (A001620).

cp's OEIS Frontend

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.

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