×

Sum of powers of integers and the additive Cauchy equation. (English) Zbl 0988.39022

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.

MSC:

39B22 Functional equations for real functions
11B25 Arithmetic progressions

Citations:

Zbl 0451.39006
PDFBibTeX XMLCite