Double-sum Rogers-Ramanujan type identities
Combinatorics
2026-05-08 v1
Abstract
As the -analog of Chebyshev polynomials, -Hermite polynomials form a cornerstone in the family of -orthogonal polynomials, which play a fundamental role in quantum algebra and mathematical physics. Recently, Andrews obtained a series of Rogers-Ramanujan type identities by constructing Bailey pairs from Chebyshev polynomials. In this paper, by applying the expansion formula of Chebyshev polynomials in terms of -Hermite polynomials and using the orthogonality relations, we derive a series of Rogers-Ramanujan type identities on double sums, which further generalized the known results due to Andrews, Shi, Sun and Yao.
Cite
@article{arxiv.2605.06248,
title = {Double-sum Rogers-Ramanujan type identities},
author = {Duanyu Chen and Xiangxin Liu and Lisa Hui Sun},
journal= {arXiv preprint arXiv:2605.06248},
year = {2026}
}