** Some Properties, Explicit Evaluations, and Applications of Ramanujan’s Remarkable Product of Theta Functions **

* Nipen Saikia*

**Abstract**

We study several properties of Ramanujan’s remarkable product of theta functions *a*_{ m,n } and establish its connections with some other parameters involving theta-functions. We also show that the explicit values of *a*_{ m,n } can be used to evaluate Ramanujan’s class invariants and some other parameters of theta functions connected with Ramanujan’s continued fractions.