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The authors aim at presenting summation formulas of Appell's function : $$ F_1 (a; b, b'; 1+ a+ b-b'+ i; 1,-1)\;(i= 0,\;{\pm} 1,\;{\pm} 2,\;{\pm} 3,\;{\pm} 4,\;{\pm} 5) $$, which, for i= 0, yields a known result due to Srivastava.