Fast algorithms for refined parameterized telescoping in difference fields

Abstract

Parameterized telescoping (including telescoping and creative telescoping) and refined versions of it play a central role in the research area of symbolic summation. In 1981 Karr introduced 7717-fields, a general class of difference fields, that enables one to consider this problem for indefinite nested sums and products covering as special cases, e.g., the (q-)hypergeometric case and their mixed versions. This survey article presents the available algorithms in the framework of ∏∑-extensions and elaborates new results concerning efficiency.