Multi-sum Rogers-Ramanujan type identities

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 2023Embargo end date: 01 Jan 2022 English Publisher:Elsevier BVJournal:Journal of Mathematical Analysis and Applications, volume 522, page 126,960 (issn: 0022-247X,

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Authors: Zhineng Cao; Liuquan Wang;

doi: 10.1016/j.jmaa.2022.126960 , 10.48550/arxiv.2205.12786

arXiv: 2205.12786

Multi-sum Rogers-Ramanujan type identities

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Abstract

We use an integral method to establish a number of Rogers-Ramanujan type identities involving double and triple sums. The key step for proving such identities is to find some infinite products whose integrals over suitable contours are still infinite products. The method used here is motivated by Rosengren's proof of the Kanade-Russell identities.

24 pages

Related Organizations

Wuhan University
China (People's Republic of)

Keywords

11P84, 33D15, 33D60, Combinatorial aspects of partitions of integers, Mathematics - Number Theory, Elementary theory of partitions, Kanade-Russell identities, integral method, Rogers-Ramanujan type identities, Mathematics - Classical Analysis and ODEs, partitions, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO), sum-product identities, Combinatorial identities, bijective combinatorics

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