DECOMPOSITION FORMULAS AND INTEGRAL REPRESENTATIONS FOR THE KAMP¶E DE F¶ERIET FUNCTION F0:3;3

By developing and using certain operators like those initiated by Burchnall-Chaundy, the authors aim at investigating several decomposition formulas associated with the Kamp¶e de F¶eriet function F0:3;3 2:0;0 [x; y]. For this purpose, many operator identities in- volving inverse pairs of symbolic operators are constructed. By employing their decomposition formulas, they also present a new group of integral representations of Eulerian type for the Kamp¶e de F¶eriet function F0:3;3 2:0;0 [x; y], some of which include several hyperge- ometric functions such as 2F1, 3F2, an Appell function F3, and the Kamp¶e de F¶eriet functions F0:3;3 2:0;0 and F0:2;31:0;1 .