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Using some formulas of S. Ramanujan, we compute in closed form the Fourier transform of functions related to Riemann zeta function $\zeta (s)=\sum \nolimits _{n=1}^{\infty } {1}/{n^{s}}$ and other Dirichlet series.

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. Resumen: Calculamos en forma cerrada integrales de ciertas expresiones que involucran una clase de series de Dirichlet. Esto es una generalización de una fórmula de Jonathan Borwein a un problema enunciado (y resuelto) por A. Ivić.

Certain finite families of rational functions have the property that the coefficients of the expansions in power series of their elements are related by simple algebraic expressions. We prove an identity in the spirit of S. Ramanujan using a result of T. N. Sinha. Fil: Panzone, Pablo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina