A344966 Decimal expansion of the sum of the reciprocals of the fourth powers of the zeros of the digamma function.

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

Offset

2,2

Comments

The sum is Sum_{k>=0} 1/x_k^4, 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=2..88.

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^4/9 + 2*gamma^2*Pi^2/3 + 4*gamma*zeta(3) + gamma^4, where gamma is Euler's constant (A001620).

Example

15.90184703322349156972084557358425176519256672643402...

Mathematica

RealDigits[Pi^4/9 + 2*EulerGamma^2*Pi^2/3 + 4*EulerGamma*Zeta[3] + EulerGamma^4, 10, 100][[1]]

Crossrefs

Cf. A344964, A344965, A344967, A344968.

Cf. A000796, A001620, A002117.

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

Sequence in context: A195144 A175997 A249205 * A294613 A144408 A371323

Adjacent sequences: A344963 A344964 A344965 * A344967 A344968 A344969

Keyword

nonn,cons

Author

Amiram Eldar, Jun 03 2021

Status

approved