Relations Between the Matrix Algebraic Factorized Type Solutions at Different Singular Points for Generalized Hypergeometric Functions of Type p+1Fp

Abstract

Recently we have presented a matrix algebraic factorization scheme for multiplicative representations of generalized hypergeometric functions of type _p+1F_p. The Method uses exponential functions with matrix arguments. We have shown that factorization is possible around any kind of point, regular or singular, and the constant matrices appearing in the argument of the exponential functions. According to the theory of linear ordinary differential equations, a series solution constructed around a point converges in the disk centered at that point with a radius equal to the difference from that point to the nearest singularity of the differential equation under consideration. Although we do not use an additive series solution, it is not hard to show that the same convergence property is expected from the factorized solutions. This paper contains the construction of the matrices transforming one evolution matrix at a singular point to another. This is done for all singularities located at z = 0, z = 1 and infinity. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)