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http://dx.doi.org/10.5666/KMJ.2015.55.4.983

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

SAIKIA, NIPEN (Department of Mathematics, Rajiv Gandhi University)
Publication Information
Kyungpook Mathematical Journal / v.55, no.4, 2015 , pp. 983-996 More about this Journal
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 $A_{k,n}$ involving Ramanujan's theta-functions ${\phi}(q)$ and ${\psi}(q)$ for any positive real numbers k and n and applied it to find explicit values of ${\psi}(q)$. As more application to the parameter $A_{k,n}$, in this paper we prove a new general theorem for explicit evaluation of Ramanujan-$G{\ddot{o}}llnitz$-Gordon continued fraction K(q) in terms of the parameter $A_{k,n}$ and give examples. We also find some new explicit values of the parameter $A_{k,n}$ and offer reciprocity theorems for the continued fraction K(q).
Keywords
Ramanujan's theta-functions; Ramanujan-$G{\ddot{o}}llnitz$-Gordon continued fraction;
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