General Theorem for Explicit Evaluations and Reciprocity Theorems for Ramanujan-Göllnitz-Gordon Continued Fraction

Abstract

In the paper A new parameter for Ramanujan's theta-functions and explicit values, Arab J. Math. Sc., 18 (2012), 105-119, Saikia studied the parameter involving Ramanujan's theta-functions and for any positive real numbers k and n and applied it to find explicit values of . As more application to the parameter , in this paper we prove a new general theorem for explicit evaluation of Ramanujan--Gordon continued fraction K(q) in terms of the parameter and give examples. We also find some new explicit values of the parameter and offer reciprocity theorems for the continued fraction K(q).