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On m-Interlacing Solutions of Linear Difference S. A. Abramov1
 

Summary: On m-Interlacing Solutions of Linear Difference
Equations
S. A. Abramov1
, M. A. Barkatou2
, D. E. Khmelnov3
1
Computing Centre of the Russian Academy of Sciences, Vavilova, 40, Moscow
119991, GSP-1 Russia; sergeyabramov@mail.ru
2
Institute XLIM, Universit´e de Limoges, CNRS, 123, Av. A. Thomas, 87060
Limoges cedex, France; moulay.barkatou@unilim.fr
3
Computing Centre of the Russian Academy of Sciences, Vavilova, 40, Moscow
119991, GSP-1, Russia; dennis khmelnov@mail.ru
Abstract. We consider linear homogeneous difference equations with ra-
tional-function coefficients. The search for solutions in the form of the m-
interlacing (1 m ord L, where L is a given operator) of finite sums of
hypergeometric sequences, plays an important role in the Hendriks­Singer
algorithm for constructing all Liouvillian solutions of L(y) = 0. We show
that Hendriks­Singer's procedure for finding solutions in the form of such

  

Source: Abramov, Sergei A. - Dorodnicyn Computing Centre of the Russian Academy of Sciences

 

Collections: Mathematics; Computer Technologies and Information Sciences