Theorems on Analogous of Ramanujan's Remarkable Product of Theta-Function and Their Explicit Evaluations

In this article, we define E-m,E-n for any positive real numbers m and n involving Ramanujan's product of theta-functions psi(-q) and f(q), which is analogous to Ramanujan's remarkable product of thetafunctions and establish its several properties by Ramanujan. We establish general theorems for the explicit evaluations of E-m,E-n and its explicit values.