A q-analogue of a formula of G.N. Watson that gives the product of two non-terminating Gaussian hypergeometric functions as a sum of two F 4 Appell series is obtained. of the many possible q-extensions of the 2 F1 function, the one that reduces to the well-known Askey-Wilson polynomial when specialized to a terminating series, is chosen. The product formula is shown to reduce to Watson's formula in the limit q → 1.

Additional Metadata
Keywords Appell function, Askey-Wilson function of the first kind, Askey-Wilson polynomials, Bailey's summation and transformation formula, Balanced and very-well-poised basic hypergeometric series, Continuous q-Jacobi polynomials, Jacobi polynomials, Product formula
Persistent URL dx.doi.org/10.1080/16073606.1999.9632057
Journal Quaestiones Mathematicae
Rahman, M. (Mizan). (1999). A q-extension of a product formula of Watson. Quaestiones Mathematicae, 22(1), 27–42. doi:10.1080/16073606.1999.9632057