A344967 Decimal expansion of Sum_{k>=0} 1/(x_k^2 - 1), where x_k is the k-th zero of the digamma function.

7, 1, 3, 4, 9, 4, 7, 2, 2, 1, 0, 9, 9, 6, 8, 1, 6, 7, 6, 9, 9, 3, 3, 5, 9, 4, 4, 4, 1, 3, 3, 3, 5, 6, 3, 6, 6, 5, 5, 3, 1, 8, 9, 3, 9, 5, 8, 5, 1, 2, 9, 5, 0, 5, 9, 4, 5, 8, 8, 7, 0, 1, 6, 5, 8, 1, 0, 4, 7, 2, 4, 0, 7, 9, 2, 1, 6, 8, 6, 8, 6, 0, 6, 1, 8, 7, 4

Offset

0,1

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=0..86.

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/(12*gamma) + gamma/2 - 1, where gamma is Euler's constant (A001620).

Example

0.71349472210996816769933594441333563665531893958512...

Mathematica

RealDigits[Pi^2/(12*EulerGamma) + EulerGamma/2 - 1, 10, 100][[1]]

Crossrefs

Cf. A344964, A344965, A344966, A344968.

Cf. A000796, A001620, A072691.

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

Sequence in context: A342377 A346103 A039616 * A362923 A201585 A089562

Adjacent sequences: A344964 A344965 A344966 * A344968 A344969 A344970

Keyword

nonn,cons

Author

Amiram Eldar, Jun 03 2021

Status

approved