An extension of the integral test

Durán, Ana; Estrada, Ricardo

doi:10.1090/S0002-9939-99-04911-4

An extension of the integral test
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by Ana Lía Durán and Ricardo Estrada PDF

Proc. Amer. Math. Soc. 127 (1999), 1745-1751 Request permission

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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