INTEGRAL REPRESENTATIONS OF APPELL'S F2, F3, HORN'S H2 AND OLSSON'S FP FUNCTIONS

. We give integral representations of Euler type for Appell’s hypergeometric functions F 2 , F 3 , Horn’s hypergeometric function H 2 and Olsson’s hypergeometric function F P . Their integrands are the same (up to a constant factor), and only the regions of integration vary. Olsson Takayama ], and Koornwinder known that Appell’s hypergeometric function F 3 , Horn’s hypergeometric function H 2 and Olsson’s hypergeometric function P also appear as solutions of . Here Appell’s F 3 , Horn’s H 2 and Olsson’s F P are analytic