Products of terminating₃F₂(1) series

It is shown that a well-known formula of Bailey for the product of two hypergeometric functions in terms of an F 4 Appell function has a discrete analogue of the form b, -x; ,b, -y (I) _ a, b : -x, y + e -y, x 4d I _ d, e : c a + b -c + 1 where x, y = 0,1, and the F-function on the right-hand side is a double hypergeometric series. Additional formulas are derived, including a discrete analogue of an important transformation formula of Watson, and discrete analogues of some more general formulas due to Burchnall and Chaundy.