| | |
Summary: ISSN 0361-7688, Programming and Computer Software, 2006, Vol. 32, No. 2, pp. 12. © Pleiades Publishing, Inc., 2006.
1
1 Linear homogeneous recurrence equations with
polynomial coefficients and systems of such equations
play a significant role in combinatorics and in the the-
ory of hypergeometric functions; the question of the
dimension of the space of solutions of such systems is
of great importance for many problems.
Let be the corresponding shift operators acting
on functions (sequences) of n1, ..., nd by f(n1, ..., ni) =
f(n1, ..., ni + 1, ..., nd), i = 1, ..., d.
Definition 1. An H-system is a system of equations
(1)
where fi, gi [n1, ..., nd]\{0} and fi, gi are coprime.
We say that a d-variate sequence T (i.e., a complex
function defined on a subset of d) is a solution of (1)
if (1) is satisfied at all those (n1, ..., ni, ..., nd) in the
domain of T for which (n1, ..., ni + 1, ..., nd) belongs to
the domain of T as well. We call a hypergeometric term
any solution T of an H-system.
|
