Double-sum Rogers–Ramanujan type identities

As the q-analog of Chebyshev polynomials, q-Hermite polynomials form a cornerstone in the family of q-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 q-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.