Fast Algorithms for Refined Parameterized Telescoping in Difference Fields
Schneider, Carsten
Original · EN
Parameterized telescoping (including telescoping and creative telescoping) and refined versions of it play a central role in the research area of symbolic summation. Karr introduced 1981 ΠΣ-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 ΠΣ-extensions and elaborates new results concerning efficiency.
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