Abstract
For any integer \(q\ge 2\) we provide a formula to express indefinite sums of a sequence \((f(n))_{n\ge 0}\) weighted by q-periodic sequences in terms of indefinite sums of sequences \((f(qn+p))_{n\ge 0}\), where \(p\in \{0,\ldots ,q-1\}\). When explicit expressions for the latter sums are available, this formula immediately provides explicit expressions for the former sums. We also illustrate this formula through some examples.
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Acknowledgements
This research is supported by the internal research Project R-AGR-0500 of the University of Luxembourg.
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Marichal, JL. On Indefinite Sums Weighted by Periodic Sequences. Results Math 74, 95 (2019). https://doi.org/10.1007/s00025-019-1022-y
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DOI: https://doi.org/10.1007/s00025-019-1022-y