Tauber, A. A theorem from the theory of infinite series. (Ein Satz aus der Theorie der unendlichen Reihen.) (German) JFM 28.0221.02 Monatsh. f. Math. 8, 273-277 (1897). Beweis des Satzes: Damit die Reihe \(\sum\limits_1^\infty a_\nu\) convergirt, ist erforderlich und hinreichend, dass gleichzeitig \(\lim\limits_{\varrho=1}\sum\limits_1^\infty a_\nu\varrho^\nu\) existirt und dass \(\lim\limits_{n=\infty}\frac1n\sum\limits_1^n \nu a_\nu=0\) ist. Reviewer: Weltzien, Prof. (Zehlendorf) Cited in 7 ReviewsCited in 59 Documents MSC: 40E05 Tauberian theorems JFM Section:Fünfter Abschnitt. Reihen. Kapitel 1. Allgemeines. Keywords:Tauberian theorems PDFBibTeX XMLCite \textit{A. Tauber}, Monatsh. Math. Phys. 8, 273--277 (1897; JFM 28.0221.02) Full Text: DOI References: [1] Kronecker, Comptes rendus, T. 103, pag. 980. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.