Representation of hypergeometric products in difference rings

Abstract

In his pioneering work [1, 2], Michael Karr introduced ΠΣ-fields which provide a rather general framework for symbolic summation. He worked out the first algorithmic steps to represent indefinite nested sums and products as transcendental extensions over a computable ground field K called the field of constants. Furthermore, he presented an algorithm that solves the parameterized telescoping problem, and as special cases the telescoping and creative telescoping problems [3] within a given ΠΣ-field.