A product of theta-functions analogous to Ramanujan's remarkable product of theta-functions and applications
Summary: We define a product \(l_{k, n}\) for any positive real numbers \(k\) and \(n\) involving Ramanujan's theta-functions \(\phi(q)\) and \(\psi(q)\) which is analogous to Ramanujan's remarkable product of theta-functions recorded by Ramanujan (1957) and study its several properties. We prove general theorems for the explicit evaluations of \(l_{k, n}\) and find some explicit values. As application of the product \(l_{k, n}\), we also offer explicit formulas for explicit values of Ramanujan's continued fraction \(V(q)\) in terms of \(l_{k, n}\) and give examples.
scientific article; zbMATH DE number 6191176
scientific article