Some q-transformation formulas and Rogers-Ramanujan type identities

2025/06/20 by Xu, Chang, Yang, Dunkun
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2506.16711

openalex publication_date 2025/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we explore the role that Liu's transformation formula can play in discovering Rogers-Ramanujan type identities. Specifically, we combine Liu's transformation formula with other q-series summations to derive a series of parameterized identities. Thereafter, through careful selection of these parameters, we obtain 75 Rogers-Ramanujan type identities from Slater's list, and uncover several new Rogers-Ramanujan type identities.

Citations

• Representations of mock theta functions
• New Proofs of Ramanujan's Identities on False Theta Functions

Related

• A general q-series transformation and its applications to multi-sum Rogers-Ramanujan-Slater identities
• Some q-Identities derived by the ordinary derivative operator
• Multidimensional Rogers-Ramanujan type identities with parameters
• Rogers-Ramanujan type identities involving double, triple and quadruple sums
• New proofs of the septic Rogers-Ramanujan identities