A modular transformation for a generalized theta function with multiple parameters

Abstract

We obtain a modular transformation for the theta function $$∑_{-∞}^{∞}∑_{-∞}^{∞}q^{a(m^2 + m^n) + cn^2 + λm + μn + ν_{ς}Am + Bn_{Z}Cm + Dn},$$ which enables us to unify and extend several modular transformations known in literature.