A Note on the Convergence of KAMPÉ DE FÉRIET's Double Hypergeometric Series

By using a technique of HORN [4], the authors discuss here the convergence conditions of the double hypergeometric series of the generalized KAMPÉ DE FÉRIET function introduced earlier by them [7]. It is shown that the recent observations of RAGAB [6] would follow fairly easily by suitably specializing the results of the present note. Also the method employed here is appropriately extended to obtain the domain of convergence of the authors' multiple hypergeometric series associated with the generalized LAURICELLA function of several variables [8].