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Theorems on analogous of Ramanujan’s remarkable product of theta-function and their explicit evaluations

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