A Product of Theta-Functions Analogous to Ramanujan's Remarkable Product of Theta-Functions and Applications. (20th December 2012)

• Record Type: Journal Article
• Authors: Saikia, Nipen
• Other Names: Pascucci Andrea Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2013(2013)
• Publication Date: 2012-12-20
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2013/620756
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : We define a product l k, n for any positive real numbers k and n involving Ramanujan's theta-functions ϕ ( q ) and ψ ( q ) which is analogous to Ramanujan's remarkable product of theta-functions recorded by Ramanujan (1957) and study its several properties. We prove general theorems for the explicit evaluations of l k, n and find some explicit values. As application of the product l k, n, we also offer explicit formulas for explicit values of Ramanujan's continued fraction V ( q ) in terms of l k, n and give examples.