Multilateral transformations of \(q\)-series with quotients of parameters that are nonnegative integral powers of \(q\) (Q2782418)

The introductory material includes some multiple-series summations by Gustafson and Milne, and four propositions which the author has established elsewhere (to appear in Sel. Math. (New Series)). The latter are ``bilateral \(q\)-IPD type transformations'' involving \(_p\psi_p\) functions. The acronym IPD refers to ordinary hypergeometiric series with Integral Parameter Differences; in the \(q\)-case pairs of upper and lower parameters appear whose quotients are integral powers of \(q\). Generalizing the four propositions, the author derives six multilateral \(q\)-IPD type transformations. They are too long to reproduce here, even though the author introduces various contracted notations. Factors of the form \({z_iq^{k_i}-z_jq^{k_j} \over z_i-z_j}\) play a significant role.NEWLINENEWLINEFor the entire collection see [Zbl 0980.00024].