M-hypergeometric solutions of linear recurrence and q-recurrence equations

الملخص EN

In this paper we consider the problem of finding m -hyper geometric solutions of anti-difference equations.

We extend the greatest factorial factorization (GFF) of a polynomial, introduced by Paule (1995), to the m -greatest factorial factorization (m GFF).

Equipped with the m GFF-concept, we present algebraically motivated approach to the problem.

This approach requires only “gcd” operations but no factorization.

Then, we solve the same problem for q -anti-difference equations.