Some New Explicit Values of Quotients of Theta-Function ϕ(q) and Applications to Ramanujan's Continued Fractions. (7th March 2013)

• Record Type: Journal Article
• Authors: Saikia, Nipen
• Other Names: Tarkhanov Nikolai Academic Editor.
• Is Part Of: Journal of complex analysis. Volume 2013(2013)
• Publication Date: 2013-03-07
• Subjects: Functions of complex variables -- Periodicals; Mathematical analysis -- Periodicals; 515.905
• DOI: 10.1155/2013/538592
• Languages: English
• ISSNs: 2314-4963

Abstract

Abstract : We find some new explicit values of the parameter h k, n for positive real numbers k and n involving Ramanujan's theta-function ϕ ( q ) 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 ϕ ( q ) by using modular equations.