A basic hypergeometric transformation of Ramanujan and a generalization
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 \((a)_{\infty}=(a,q)_{\infty}=\prod^{\infty}_{n=0}(1-aq^ n)\).
scientific article; zbMATH DE number 3959959