A note on a theorem concerning series of positive terms. Extract from a letter of Prof. E. Landau to Prof. I. Schur (communicated by G. H. Hardy). (Q1450134)
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scientific article; zbMATH DE number 2586070
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on a theorem concerning series of positive terms. Extract from a letter of Prof. E. Landau to Prof. I. Schur (communicated by G. H. Hardy). |
scientific article; zbMATH DE number 2586070 |
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A note on a theorem concerning series of positive terms. Extract from a letter of Prof. E. Landau to Prof. I. Schur (communicated by G. H. Hardy). (English)
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1926
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Der Brief ist am 22. Juni 1921 geschrieben und enthält einen Beweis der Ungleichung \[ \left(\frac{\varkappa}{\varkappa-1}\right)^{\varkappa}\sum_1^N a_n^{\varkappa} \geqq\sum_1^N\left(\frac{A_n}n\right)^{\varkappa}\quad \left(a_n\geqq 0, \;\varkappa>1 \;A_n=\sum_{\nu=1}^n a_{\nu} \right), \] in der für jedes endliche \(N\) und \(N=\infty\) das Gleichheitszeichen nur gilt, wenn alle \(a_n = 0\) sind; \(\left(\dfrac{\varkappa}{\varkappa-1}\right)^{\varkappa}\) ist die wahre Konstante. (Vgl. \textit{Hardy} 1918, 1920, 1925; F. d. M. 46, 410 (JFM 46.0410.*); 47, 207; 51, 192.) (IV 2.)
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