DECOMPOSITION FORMULAS AND INTEGRAL REPRESENTATIONS FOR THE KAMP´E DE F´ERIET FUNCTION F 0:3;3 2:0;0 [x, y]

Abstract

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 F 0:3;3 2:0;0 [x, y]. For this purpose, many operator identities involving 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 F 0:3;3 2:0;0 [x, y], some of which include several hypergeometric functions such as 2F1, 3F2, an Appell function F3, and the Kamp´e de F´eriet functions F 0:3;3

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