On the reduction of linear systems of difference equations

摘要

This paper deals with linear systems of difference equations whose coefficients admit generalized factorial series representations at z = ∞. We shall give a criterion by which a given system is determined to have a regular singularity.

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In the same manner, we give an algorithm, implementable in a computer algebra system, which reduces in a finite number of steps the system of difference equations on an irreducible form.