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Journal of Complex Analysis
Volume 2013, Article ID 538592, 7 pages
http://dx.doi.org/10.1155/2013/538592
Research Article

Some New Explicit Values of Quotients of Theta-Function and Applications to Ramanujan's Continued Fractions

Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh, Arunachal Pradesh 791112, India

Received 14 November 2012; Accepted 23 January 2013

Academic Editor: Nikolai Tarkhanov

Copyright © 2013 Nipen Saikia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We find some new explicit values of the parameter for positive real numbers and involving Ramanujan's theta-function and give some applications of these new values for the explicit evaluations of Ramanujan's continued fractions. In the process, we also establish two new identities for by using modular equations.