Some $q$-transformation formulas and Rogers-Ramanujan type identities
Chang Xu, Dunkun Yang
TL;DR
This paper uses Liu's transformation formula combined with $q$-series summations to derive and discover numerous Rogers-Ramanujan type identities, including 75 from Slater's list and several new ones.
Contribution
It introduces a novel method of combining Liu's transformation with $q$-series to systematically generate and identify Rogers-Ramanujan type identities.
Findings
Derived 75 identities from Slater's list
Discovered several new Rogers-Ramanujan type identities
Showed the effectiveness of Liu's transformation in identity discovery
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 -series summations to derive a series of parameterized identities. Thereafter, through careful selection of these parameters, we obtain Rogers-Ramanujan type identities from Slater's list, and uncover several new Rogers-Ramanujan type identities.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical functions and polynomials · Advanced Mathematical Theories and Applications