On certain continued fractions related to \(_2\Psi_2\) basic bilateral hypergeometric functions (Q1860673)

Continued fractions are developed for the quotients \[ {_2\psi_2 \left( \begin{matrix} aq, & b \\ c & d \end{matrix}; x\right) \over_2\psi_2 \left( \begin{matrix} a,b\\ c,d \end{matrix}; x\right)} \quad\text{and}\quad {_2\psi_2\left( \begin{matrix} a, & bq\\ c, & d\end{matrix}; x\right)}. \] Some special cases in which the \(_2\psi_2\) functions reduce to \(_2\varphi_1\) or \(_2F_1\), and further special cases of these functions, are given. Convergence of the continued fractions is not analyzed. The authors claim that some of their results seem to be new, but unfortunately they do not say which ones.