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Revista Colombiana de Matemáticas

versão impressa ISSN 0034-7426

Rev.colomb.mat. vol.54 no.1 Bogotá jan./jun. 2020

https://doi.org/10.15446/recolma.v54n1.89775 

Original articles

Integrals of certain Dirichlet series

Integrales de ciertas series de Dirichlet

Pablo A. Panzone1  * 

1Universidad Nacional del Sur, Bahía Blanca, Argentina


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.

Keywords: Dirichlet Series; Integrals

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.

Palabras clave: Integrales; Series de Dirichlet

Full text available only in PDF format.

REFERENCES

[1] J. Borwein, A Class of Dirichlet Series Integrals, The American Mathematical Monthly 114 (2007), 70-76. [ Links ]

[2] I. D. Gradshteyn and I. M. Ryzhik, Table of integrals series and products, Academic Press, 1965. [ Links ]

[3] A. Ivić, Solution to a Monthly Problem # 10939, proposed by A. Ivić, with his solution in The American Mathematical Monthly 110 (2003), 847-848. [ Links ]

Received: August 13, 2019; Accepted: September 16, 2019

*Correspondencia: Pablo A. Panzone, Departamento e Instituto de Matemática, Universidad Nacional del Sur, Av. Alem 1253, (8000) Bahía Blanca, Argentina. Correo electrónico: pablopanzone@hotmail.com. DOI: https://doi.org/10.15446/recolma.v54n1.89775

2010 Mathematics Subject Classification. 11M99, Supported in part by UNS and CONICET.

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License