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arXiv · 2506.16711

Some $q$-transformation formulas and Rogers-Ramanujan type identities

Chang Xu·Dunkun Yang
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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.

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Chang Xu, Dunkun Yang. 2025-06-20. Some $q$-transformation formulas and Rogers-Ramanujan type identities. https://arxiv.org/abs/2506.16711

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