A basic hypergeometric transformation of Ramanujan and a generalization
type: Item
instance of: scholarly article
title: A basic hypergeometric transformation of Ramanujan and a generalization
zbMATH Open document ID: 0596.33005
author: B. George
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1986-01-01T00:00:00Z
review text: By considering the following hypergeometric series \[ (- bq)_{\infty}\sum^{\infty}_{n=0}\frac{q^{n(n+1)/2} (-(\lambda /a))_ na^ n}{(q\quad)_ n(-bq)_ n}, \] the authors give yet another proof of the well-known transformation due to Ramanujan: \[ (- bq)_{\infty}\sum^{\infty}_{n=0}\frac{q^{n^ 2}\lambda^ n}{(q)_ n(-bq)_ n}=\sum^{\quad \infty}_{n=0}\frac{q^{n(n+1)/2} (-(\lambda /b))_ nb^ n}{(q)_ n}, \] where \((a)_{\infty}=(a,q)_{\infty}=\prod^{\infty}_{n=0}(1-aq^ n)\).
Mathematics Subject Classification ID: 33D05
zbMATH DE Number: 3959959
zbMATH Keywords: basic hypergeometric series
zbMATH Keywords: Euler's formula
zbMATH Keywords: Ramanujan
reviewed by: Ajendra Nath Srivastava
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3959959