Abstract
AbstractParameterized 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 \(\varPi \varSigma \)-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 \(\varPi \varSigma \)-extensions and elaborates new results concerning efficiency.KeywordsRational PartConstant FieldDifference FieldLinear Difference EquationGround FieldThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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