Characterization of regular singular linear systems of difference equations |
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Authors: | M A Barkatou |
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Institution: | (1) Département de Mathématiques, Faculté des Sciences, 123 Avenue Albert Thomas, 87000 Limoges-Cedex, France |
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Abstract: | This paper deals with linear systems of difference equations whose coefficients admit generalized factorial series representations atz= . We are concerned with the behavior of solutions near the pointz= (the only fixed singularity for difference equations). It is important to know whether a system of linear difference equations has a regular singularity or an irregular singularity. To a given system ( ) we can assign a number , called the Moser's invariant of ( ), so that the system is regular singular if and only if ![mgr](/content/u74155j861550611/xxlarge956.gif) 1. We shall develop an algorithm, implementable in a computer algebra system, which reduces in a finite number of steps the system of difference equations to an irreducible form . The computation ot the number can be done explicitly from this irreducible form . |
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Keywords: | AMS (M08) |
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