Certain results involving \(q\)-series and continued fractions (Q2751695)

Starting with an earlier continued fraction expansion for the ratio NEWLINE\[NEWLINE_3\Phi_2\left[{a,b,c;\frac{de}{abc}\atop d,e}\right]\Biggl/{_3\Phi_2}\left[{aq,b,c;\frac{de}{abc}\atop dq,e}\right] NEWLINE\]NEWLINE of basic hypergeometric series, and a known transformation for such series \(_3\Phi_2\), the paper establishes continued fraction expansions for NEWLINE\[NEWLINE \frac{(\frac eb, \frac ec; q)_\infty}{(\frac eq, \frac{eq}{bc}; q)_\infty} \quad\text{and}\quad \frac{(\frac eb, \frac ec; q)_\infty}{(\frac eq, \frac{e}{bc}; q)_\infty}. NEWLINE\]NEWLINE Particular choices of \(e, b\) and \(c\) and letting \(q\to 1\) reduce these results to entries 33 and 25 of Chapter 12 in Ramanujan's 2. notebook.NEWLINENEWLINEFor the entire collection see [Zbl 0970.00018].