Extensions of two q-series expansions with applications to biorthogonal rational functions

摘要

In this paper, we derive two most general possible q-hypergeometric expansion formulae for 12Φ11(q) and rΦs(z), respectively. The results are unique in the sense that no such results are available in the literature beyond 4Φ3(q) so far and have the advantage that these results are also applicable to the top-level 10Φ9(q) biorthogonal rational functions.