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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].

A NEW PROOF OF A REDUCTION FORMULA FOR THE APPELL SERIES <em>F</em><sub>3</sub> DUE TO BAILEY