A Q-EXTENSION OF A PRODUCT FORMULA OF WATSON

Abstract

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.