It is shown that a
well-known formula of Bailey for the product of two hypergeometric functions in
terms of an F4 Appell function has a discrete analogue of the form
(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.
![[ ] [ ]
a,b,− x; a,b,− y;
3F2 c,d 3F2 a +b − c+ 1,e
[a,b : − x,y + e;− y,x+ d;]
= F d,e : c;a+ b− c+ 1; .](a080x.png)
