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A Product of Theta-Functions Analogous to Ramanujan's Remarkable Product of Theta-Functions and Applications

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  • Nipen Saikia

Abstract

We define a product for any positive real numbers and involving Ramanujan's theta-functions and 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 and find some explicit values. As application of the product , we also offer explicit formulas for explicit values of Ramanujan's continued fraction in terms of and give examples.

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  • Nipen Saikia, 2013. "A Product of Theta-Functions Analogous to Ramanujan's Remarkable Product of Theta-Functions and Applications," Journal of Mathematics, Hindawi, vol. 2013, pages 1-5, December.
    • Handle: RePEc:hin:jjmath:620756
    DOI: 10.1155/2013/620756
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