IJPAM: Volume 74, No. 4 (2012)
Department of Mathematics
Central College Campus
Bangalore, 560 001, INDIA
Abstract. In his `lost' notebook, S. Ramanujan introduced the parameter related to the Rogers - Ramanujan continued fraction . In this paper, we establish some new modular equations of degree 5. We establish some general formulas for the explicit evaluations of the ratios of Ramanujan's theta function . We obtain several new modular relations connecting with for different positive integer reciprocity theorems and also compute several new explicit evaluations.
Received: August 18, 2011
AMS Subject Classification: 33D20, 11F55, 11S23
Key Words and Phrases: continued fraction, modular equation, reciprocity theorem, theta function
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395