Rising greatest factorial factorization for Gosper's algorithm

الملخص EN

In this paper we define the "rising greatest factorial factorization" (RGFF) of polynomials.

It is a canonical form representation which can be viewed as an analogue to the greatest factorial factorization (GFF) [V.Z.

Gathen and J.

Gerhard, 1999, P.Paule, 1995], but with a positive integer shifts instead of negative integer shifts.

We give lemma to compute the RGFF for any polynomial.

We use this canonical representation and greatest common devisor (gcd) concept to give an approach for Gosper’s algorithm [R.W, Jr.

Gosper, 1978].