Abstract
We compute in closed form the integrals of certain expressions involving a class of Dirichlet series. This is a generalization of a formula of Jonathan Borwein to a problem stated (and solved) by A. Ivić.
Highlights
We write as usual s = σ + it with σ, t real numbers and let ζ(s) =
Borwein proved that the integrals of expressions involving a certain class of Dirichlet series could be evaluated [1]
The last equality follows observing that the inner sum in the last equation with m = 1 is zero and
Summary
Calculamos en forma cerrada integrales de ciertas expresiones que involucran una clase de series de Dirichlet. Esto es una generalizacion de una formula de Jonathan Borwein a un problema enunciado (y resuelto) por A. We write as usual s = σ + it with σ, t real numbers and let ζ(s) = A. Ivic [3] proved the following remarkable integral evaluation:
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