Dandan Chen, Tianjian Xu, “On Bilateral Multiple Sums and Rogers–Ramanujan Type Identities”, SIGMA, 2026, Volume 22,038, 12 pp.

On Bilateral Multiple Sums and Rogers–Ramanujan Type Identities

Dandan Chen^ab, Tianjian Xu^a

^a Department of Mathematics, Shanghai University, P.R. China
^b Newtouch Center for Mathematics, Shanghai University, P.R. China

Abstract: We establish some new bilateral double-sum Rogers–Ramanujan identities involving parameters. As applications, these identities yield several new multi-sum Rogers–Ramanujan type identities. Our proofs utilize the theory of basic hypergeometric series in conjunction with the integral method.

Keywords: Rogers–Ramanujan type identities, bilateral summations, multiple sums, $q$-series, integral method.

MSC: 11P84, 33D60

Received: October 21, 2025; in final form March 29, 2026; Published online April 18, 2026

Language: English

DOI: 10.3842/SIGMA.2026.038