A NEW PROOF OF A REDUCTION FORMULA FOR THE APPELL SERIES F 3 DUE TO BAILEY

In this short note, we provide a new proof of an interesting and useful reduction formula for the Appell series $F_{3}$  due to Bailey [{\it On the sum of a terminating ${}_3F_2(1)$}, Quart. J. Math. Oxford Ser. (2) {\bf4} (1953), 237--240].