m-Hypergeometric Solutions of Anti-Difference and q -Anti-Difference Equations
Abstract
In this paper we consider the problem of finding m -hypergeometricsolutions of anti-difference equations. We extend the greatest factorialfactorization (GFF) of a polynomial, introduced by Paule (1995), to the m -greatest factorial factorization ( GFF). Equipped with the GFF-concept, wepresent algebraically motivated approach to the problem. This approach requiresonly “gcd” operations but no factorization. Then, we solve the same problem for-anti-difference equations.m mq
Keywords
Gosper’s algorithm, m -hypergeometric solution, m-greatest factorial factorization, q -Gosper algorithm, qm -hypergeometric solution, qm -greatest factorial factorization.Metrics