Vol. 56, No. 1, 1975

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Products of terminating 3F2(1) series

George Gasper, Jr.

Vol. 56 (1975), No. 1, 87–95
Abstract

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

   [       ]   [            ]
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; .
(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.

Mathematical Subject Classification
Primary: 33A30
Milestones
Received: 23 September 1973
Published: 1 January 1975
Authors
George Gasper, Jr.