Eta-Quotient Representations for a Three Parameter Family of Modular Functions Associated with the Rogers-Ramanujan Continued Fraction

Abstract

In 2021, Chern and Tang introduced two families of two-parameter modular functions associated with the Rogers-Ramanujan continued fraction. They established recurrence relations that express the members of these families in terms of eta quotients, and used these expressions to obtain dissection formulas. Motivated by their work, we construct a three-parameter extension and derive the corresponding recursive eta quotient representations. Our result also has applications to dissection formulas. In particular, it is used in separate work to obtain $5$-dissection formulas for overpartitions with restricted odd differences.