TY - JOUR T1 - Symmetry of terminating basic hypergeometric series representations of the Askey–Wilson polynomials AU - Cohl, Howard S. AU - Costas-Santos, Roberto S. JO - Journal of Mathematical Analysis and Applications VL - 517 IS - 1 SP - 126583 PY - 2023 DA - 2023/01/01/ SN - 0022-247X DO - https://doi.org/10.1016/j.jmaa.2022.126583 UR - https://www.sciencedirect.com/science/article/pii/S0022247X22005972 KW - Basic hypergeometric series KW - Basic hypergeometric orthogonal polynomials KW - Basic hypergeometric transformations AB - In this paper, we explore the symmetric nature of the terminating basic hypergeometric series representations of the Askey–Wilson polynomials and the corresponding terminating basic hypergeometric transformations that these polynomials satisfy. In particular we identify and classify the set of 4 and 7 equivalence classes of terminating balanced ϕ34 and terminating very-well-poised W78 basic hypergeometric series which are connected with the Askey–Wilson polynomials. We study the inversion properties of these equivalence classes and also identify the connection of both sets of equivalence classes with the symmetric group S6, the symmetry group of the terminating balanced ϕ34. We then use terminating balanced ϕ34 and terminating very-well poised W78 transformations to give a broader interpretation of Watson's q-analog of Whipple's theorem and its converse. ER -