Residues and Telescopers for Rational Functions

Details Residues and Telescopers for Rational Functions Residues and Telescopers for Rational Functions

2012-03-19

arxiv.org/abs/1203.4200v1

Mathematics

Combinatorics

30 pages

Scientific paper

We give necessary and sufficient conditions for the existence of telescopers for rational functions of two variables in the continuous, discrete and q-discrete settings and characterize which operators can occur as telescopers. Using this latter characterization, we reprove results of Furstenberg and Zeilberger concerning diagonals of power series representing rational functions. The key concept behind these considerations is a generalization of the notion of residue in the continuous case to an analogous concept in the discrete and q-discrete cases.

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