An elementary proof by mathematical induction of the equivalence of the Cesàro and Hölder sum formulas. (Q1445123)
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scientific article; zbMATH DE number 2581470
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An elementary proof by mathematical induction of the equivalence of the Cesàro and Hölder sum formulas. |
scientific article; zbMATH DE number 2581470 |
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An elementary proof by mathematical induction of the equivalence of the Cesàro and Hölder sum formulas. (English)
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1927
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Verf. erhält durch Induktion von \(r\) auf \(r + 1\) Formeln, die (1) \(H_n^{(r)}\) mit Hilfe von \(C_p^{(r)}\), (\(p = 0,1,2, \ldots, n\)), (2) \(C_n^{(r)}\) mit Hilfe von \(H_p^{(r)}\), (\(p = 0, 1, 2, \ldots, n\)) ausdrücken; dabei bedeutet \(r\) eine natürliche Zahl. Alsdann wird für diesen Fall die Äquivalenz der beiden Summationsverfahren bewiesen.
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