On indefinite sums weighted by periodic sequences

04/17/2018

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by   Jean-Luc Marichal, et al.

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For any integer q≥ 2 we provide a formula to express indefinite sums of a sequence (f(n))_n≥ 0 weighted by q-periodic sequences in terms of indefinite sums of sequences (f(qn+p))_n≥ 0, where p∈{0,...,q-1}. When explicit expressions of the latter sums are available, this formula immediately provides explicit expressions of the former sums. We also illustrate this formula through some examples.