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Rational solutions of linear di#erence and qdi#erence equations with polynomial coe#cients #
 

Summary: Rational solutions of linear di#erence and q­di#erence
equations with polynomial coe#cients #
S.A.Abramov
Computer Center of the Russian Academy of Science
Vavilova 40, Moscow 117967, Russia
abramov@ccas.ru
Abstract
We propose a simple algorithm to construct a polynomial divisible by the denomi­
nator of any rational solution of a linear di#erence equation
a n (x)y(x + n) + . . . + a 0 (x)y(x) = b(x)
with polynomial coe#cients and a polynomial right­hand side. Then we solve the same
problem for q­di#erence equations.
Nonhomogeneous equations with hypergeometric right­hand sides are considered as
well.
§1.Di#erence equations
Consider the problem of finding all rational solutions of linear di#erence equations of the
form
a n (x)y(x + n) + . . . + a 0 (x)y(x) = b(x) (1)
or in operator form, Ly(x) = b(x), where
L = a n (x)E n + . . . + a 1 (x)E + a 0 (x). (2)

  

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

 

Collections: Mathematics; Computer Technologies and Information Sciences