English

Rogers-Ramanujan type identities involving double, triple and quadruple sums

Combinatorics 2023-08-02 v2 Number Theory

Abstract

We prove a number of new Rogers-Ramanujan type identities involving double, triple and quadruple sums. They were discovered after an extensive search using Maple. The main idea of proofs is to reduce them to some known identities in the literature. This is achieved by direct summation or the constant term method. We also obtain some new single-sum identities as consequences.

Keywords

Cite

@article{arxiv.2306.17085,
  title  = {Rogers-Ramanujan type identities involving double, triple and quadruple sums},
  author = {Zhi Li and Liuquan Wang},
  journal= {arXiv preprint arXiv:2306.17085},
  year   = {2023}
}

Comments

50 pages. We added Remarks 1 and 2 and some more general formulas such as (4.53)-(4.54). Some formulas in the first version were deleted since they are special cases of these new parameterized identities