A product of theta-functions analogous to Ramanujan's remarkable product of theta-functions and applications
type: Item
instance of: scholarly article
title: A product of theta-functions analogous to Ramanujan's remarkable product of theta-functions and applications
zbMATH Open document ID: 1275.11075
DOI: 10.1155/2013/620756
author: Nipen Saikia
published in: Journal of Mathematics
publication date: 2013-07-25T00:00:00Z
review text: Summary: We define a product \(l_{k, n}\) for any positive real numbers \(k\) and \(n\) involving Ramanujan's theta-functions \(\phi(q)\) and \(\psi(q)\) 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.
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 33E05
zbMATH DE Number: 6191176
Wikidata QID: Q59015594
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/620756
OpenAlex ID: W2035546061
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description: scientific article; zbMATH DE number 6191176