This work attempts to determine how the generalized hypergeometric function of F-p(p) type behaves when its argument tends to infinity. To this end we use the vector differential equation constructed by reducing the order and increasing the number of the unknowns by appropriate definitions. This vector differential equation as it stands does not permit us to match the expansions at zero and infinite values of the independent variable because infinity is the irregular singular point of the differential equation. This urges us to use a transform to get singular points in the resulting equation which are regular at most. This work constructs a constant transform matrix between the solutions at zero and infinity. (c) 2004 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim.