## 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)

### MSC:

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