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An extension of the integral test


Authors: Ana Lía Durán and Ricardo Estrada
Journal: Proc. Amer. Math. Soc. 127 (1999), 1745-1751
MSC (1991): Primary 26A06, 40A10, 46F10
DOI: https://doi.org/10.1090/S0002-9939-99-04911-4
Published electronically: February 11, 1999
MathSciNet review: 1610952
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Abstract | References | Similar Articles | Additional Information

Abstract: We identify a class of functions for which an extension of the well known integral test holds, namely, the series $\sum _{k=1}^{\infty }\phi (k)$ is Cesàro summable if and only if the integral $\int _{1}^{\infty }\phi (x)\,dx$ is. We also give the corresponding multidimensional results.


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Additional Information

Ana Lía Durán
Affiliation: Escuela de Matemática, Universidad de Costa Rica, 2060 San José, Costa Rica
Email: analiad@emate.ucr.ac.cr

Ricardo Estrada
Affiliation: Escuela de Matemática, Universidad de Costa Rica, 2060 San José, Costa Rica
Email: restrada@cariari.ucr.ac.cr

DOI: https://doi.org/10.1090/S0002-9939-99-04911-4
Keywords: Integral, series, summability
Received by editor(s): September 12, 1997
Published electronically: February 11, 1999
Communicated by: Frederick W. Gehring
Article copyright: © Copyright 1999 American Mathematical Society

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