On some new modular relations for a remarkable product of theta--functions

Abstract

In this paper, we establish some new modular equations of degree 9. We also establish several new P -Q mixed modular equations involving theta-functions which are similar to those recorded by Ramanujan in his notebooks. As an application, we establish some new general formulas for explicit evaluations of a Remarkable product of theta-functions.

On relationships between q-products identities, Ralpha, Rbeta and Rm functions related to Jacobi's triple-product identity

“…. Each of the following preliminary results will be needed for the demonstration of our main results in this paper (see [11]):…”