NEW MODULAR IDENTITIES AND PARTITION INTERPRETATIONS FOR SEPTIC ROGERS-RAMANUJAN FUNCTIONS

Abstract

The septic RogersRamanujan functions A(q), B(q), and C(q) serve as natural counterparts of the
classical RogersRamanujan functions and are signicant in the study of theta functions and modular
identities. Building upon Hahn's ground breaking research, other modular relations concerning these
functions have been derived using Ramanujan's theory of theta functions. This work presents an
extensive array of novel modular relations pertaining to the septic RogersRamanujan functions.
Through the methodical application of identities related to Ramanujans general theta function,
alongside transformation formulae and decomposition methods, we construct several families of
modular relations of diering degrees. These ndings substantially enhance the current literature
and provide a cohesive framework for deriving further identities related to septic RogersRamanujan
functions