INTEGRAL REPRESENTATIONS FOR HORN'S H₂ FUNCTION AND OLSSON'S F_P FUNCTION

摘要

We derive some Euler type double integral representations for hypergeometricfunctions in two variables. In the first part of this paper we deal with Horn's$H_2$ function, in the second part with Olsson's $F_P$ function. Our doubleintegral representing the $F_P$ function is compared with the formula for thesame integral representing an $H_2$ function by M. Yoshida (1980) and M. Kita(1992). As specified by Kita, their integral is over a twisted cycle. Wepresent a classical double integral version of Kita's integral, with outerintegral over a Pochhammer double loop, which we can evaluate as $H_2$ just asKita did for his integral. Then we show that shrinking of the double loopyields a sum of two double integrals for $F_P$.