School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Hadamard products for generalized Rogers–Ramanujan series
Document Type
Article
Publication Date
4-1-2008
Abstract
The purpose of this paper is to derive product representations for generalizations of the Rogers–Ramanujan series. Special cases of the results presented here were first stated by Ramanujan in the “Lost Notebook” and proved by George Andrews. The analysis used in this paper is based upon the work of Andrews and the broad contributions made by Mourad Ismail and Walter Hayman. Each series considered is related to an extension of the Rogers–Ramanujan continued fraction and corresponds to an orthogonal polynomial sequence generalizing classical orthogonal sequences. Using Ramanujan's differential equations for Eisenstein series and corresponding analogues derived by V. Ramamani, the coefficients in the series representations of each zero are expressed in terms of certain Eisenstein series.
Recommended Citation
Huber, Tim. "Hadamard products for generalized Rogers–Ramanujan series." Journal of approximation theory 151.2 (2008): 126-154. https://doi.org/10.1016/j.jat.2007.09.005
Publication Title
Journal of Approximation Theory
DOI
10.1016/j.jat.2007.09.005
Comments
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