On indefinite sums weighted by periodic sequences

Jean-Luc Marichal

Published 2018-04-17Version 1

For any integer $q\geq 2$ we provide a formula to express indefinite sums of a sequence $(f(n))_{n\geq 0}$ weighted by $q$-periodic sequences in terms of indefinite sums of sequences $(f(qn+p))_{n\geq 0}$, where $p\in\{0,\ldots,q-1\}$. 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.