CONNECTION FORMULAS RELATED WITH APPELL'S <i>F</i>₂, HORN'S <i>H</i>₂AND OLSSON'S <i>F</i><i>_P</i>FUNCTIONS

Abstract

Some of the connection problems associated with the system of differential equations E 2 , which is satisfied by Appell's F 2 function, are solved by using integrals of Euler type. The present results give another proof of connection formulas related with Appell's F 2 , Horn's H 2 and Olsson's F P functions, which are obtained by Olsson.

On the evaluation of the Appell F2 double hypergeometric function

“…It should be noted that several authors have already studied the transformation theory and analytic continuation properties 2 of F 2 . One can for instance mention the remarkable analysis of [22], the recent references [23][24][25][26] (see also references therein), or the more classical works [27,28]. For particular values of the parameters of F 2 we refer the reader to [29][30][31].…”