Name: On Indefinite Sums Weighted by Periodic Sequences
Creator: Jean-Luc Marichal
Keywords: : Computer science [C05] [Engineering, computing & technology], FOS: Computer and information sciences, Mathematics - Number Theory, Discrete Mathematics (cs.DM), harmonic number, Primary 05A19, 39A70, Secondary 05A15, anti-difference, : Sciences informatiques [C05] [Ingénierie, informatique & technologie], generating function, FOS: Mathematics

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 30 Apr 2019Embargo end date: 01 Jan 2018 English Publisher:Springer Science and Business Media LLCJournal:Results in Mathematics, volume 74 (issn: 1422-6383, eissn: 1420-9012,

Authors: Jean-Luc Marichal;

doi: 10.1007/s00025-019-1022-y , 10.48550/arxiv.1804.06418

arXiv: http://arxiv.org/abs/1804.06418

On Indefinite Sums Weighted by Periodic Sequences

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Abstract

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 for the latter sums are available, this formula immediately provides explicit expressions for the former sums. We also illustrate this formula through some examples.

Related Organizations

University of Luxembourg
Luxembourg

Keywords

: Computer science [C05] [Engineering, computing & technology], FOS: Computer and information sciences, Mathematics - Number Theory, Discrete Mathematics (cs.DM), harmonic number, Primary 05A19, 39A70, Secondary 05A15, anti-difference, : Sciences informatiques [C05] [Ingénierie, informatique & technologie], generating function, FOS: Mathematics, : Mathematics [G03] [Physical, chemical, mathematical & earth Sciences], Mathematics - Combinatorics, : Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre], Combinatorics (math.CO), Number Theory (math.NT), Indefinite sum, periodic sequence, Computer Science - Discrete Mathematics

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