An Exponential Matrix Product Based Representation for Generalized Hypergeometric Functions of Type pFp

In this work, a new representation is developed for generalized hypergeometric functions of type _pF_p. To this end a first order vector differential equation is constructed in a way such that the derivative of the unknown vector has unit matrix coefficient. The solution vector differential equation is rewritten in the form of a series expansion. An infinite process of factor extractions and annihilations is employed to construct finally a vector differential equation that can be easily solved. Truncation of this scheme can be used to get approximations to hypergeometric functions of type _pF_p. A simple, yet meaningful, implementation seems to give quite promising results. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)