$q$-Analogues of two product formulas of hypergeometric functions by Bailey

We use Andrews’ $q$-analogues of Watson’s and Whipple’s ${}_3{F}_2$ summation theorems to deduce two formulas for products of specific basic hypergeometric functions. These constitute $q$-analogues of corresponding product formulas for ordinary hypergeometric functions given by Bailey. The first formula was obtained earlier by Jain and Srivastava by a different method.