Structural Insights into Mock Theta-Function Identities via Multivariable R-Functions and Partition Theory

Abstract

This paper introduces five new identities involving eighth-order mock theta functions, expressed in terms of multivariable R-functions. These identities are derived using the well-known qɩ-product identities in conjunction with the classical Jacobi triple product identity. The results establish profound links between theta function representations and combinatorial partition theory. Specifically, we present key findings that offer structural insight into mock theta function identities, using multivariate R-functions and partition theory. These discoveries uncover new patterns and identities within the framework of mock theta functions, with a particular focus on their multivariable structure and their connections to partition theory. In addition, we concisely summarize recent advancements in the field and discuss potential applications. The findings emphasize a significant relationship between our results and partition-theoretic identities. © 2025, Jangjeon Research Institute for Mathematical Sciences and Physics. All rights reserved.