On the Pringsheim convergence of double series. (English) Zbl 1206.40004

The authors investigate, in analogy with some well-known results for single series, several aspects of the convergence of a double series of real numbers in the sense of Pringsheim. Also, some of the gaps in some previous study are filled as regards the convergence of a double series.
They give some tests for absolute convergence of a double series including analogues of Cauchy’s Condensation Test, Abel’s \(k\)th Term Test, Limit Comparison Test, Ratio Test, Ratio Comparison Test, and Raabe’s Test. Moreover, they examine criteria for convergence of the Cauchy product for two double series.
Reviewer: Umit Totur (Aydin)


40B05 Multiple sequences and series
40A05 Convergence and divergence of series and sequences
40G05 Cesàro, Euler, Nörlund and Hausdorff methods
Full Text: DOI