Closed form general solution of the hypergeometric matrix differential equation

Authors:
L. Jódar;J. C. Cortés
Affiliations:
Departamento de Matemática Aplicada Universidad Politécnica de Valencia P.O. Box 22.012 Valencia, Spain;Departamento de Matemática Aplicada Universidad Politécnica de Valencia P.O. Box 22.012 Valencia, Spain
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2000

Citing 2
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Abstract

In this paper, the hypergeometric matrix differential equation z(1 - z)W'' - zAW' + W'(C - z(B + I)) - AWB = 0 is studied. First it is proved that if matrix C is invertible and no negative integer is one of its eigenvalues, then the hypergeometric matrix function F(A, B; C; z) is an analytic solution in the unit disc. If, apart from the above hypothesis on C, matrices A and B commute with C, then a closed form general solution is expressed in terms of F(A, B; C; z) and F(A + I - C, B + I - C; 2I - C; z)z^I^ ^-^ ^C in @W(@d) = z @e D"0, 0 0 is a positive number determined in terms of the data.