Double Series and Convergence Tests

M. Mursaleen and S. A. Mohiuddine
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M. Mursaleen: Aligarh Muslim University, Department of Mathematics
S. A. Mohiuddine: King Abdulaziz University, Department of Mathematics

Chapter Chapter 9 in Convergence Methods for Double Sequences and Applications, 2014, pp 149-166 from Springer

Abstract: Abstract Since Pringsheim introduced the notion of convergence of a numerical double series in terms of the convergence of the double sequence of its rectangular partial sums. However, an exhaustive treatment giving analogues of all well-known convergence aspects of single series seems to be unavailable. In this chapter, we give results to fill in some of the gaps in such a treatment and also to point out some errors in previous attempts to obtain results exactly analogous to those of a single series.

Keywords: Double series; Cauchy’s condensation test; Abel’s kth term test; Limit comparison test; Ratio test; Ratio comparison test; Raabe’s test; Cauchy product double series; Test for absolute convergence of a double series (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-1611-7_9

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DOI: 10.1007/978-81-322-1611-7_9

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