Sum of powers of integers and the additive Cauchy equation (Q2739281)
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scientific article; zbMATH DE number 1643748
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sum of powers of integers and the additive Cauchy equation |
scientific article; zbMATH DE number 1643748 |
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23 June 2002
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Cauchy's functional equation
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sum of powers on arithmetic progressions
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sums of products
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Sum of powers of integers and the additive Cauchy equation (English)
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The author presents another variant of applying Cauchy's functional equation to generate closed expressions for \(n\)-term sums of \(m\)-th powers of consecutive terms in an algebraic progression [cf. the reviewer, Aequationes Math. 21, 39-43 (1980; Zbl 0451.39006)], this time for \(n=4\), \(n=5\), the arithmetic progressions being \(1,2,\dots,n\) and \(1,3,5,\dots,2n-1\). A similar method is applied to sums of products.
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