Telescopers for Rational and Algebraic Functions via Residues

Abstract

We show that the problem of constructing telescopers for functions of m variables is equivalent to the problem of constructing telescopers for algebraic functions of m -1 variables and present a new algorithm to construct telescopers for algebraic functions of two variables. These considerations are based on analyzing the residues of the input. According to experiments, the resulting algorithm for rational functions of three variables is faster than known algorithms, at least in some examples of combinatorial interest. The algorithm for algebraic functions implies a new bound on the order of the telescopers.

References in corpus (2)

• A Fast Approach to Creative Telescoping
• Explicit formula for the generating series of diagonal 3D rook paths

Cited by in corpus (5)

• Diagonals of rational functions, pullbacked 2F1 hypergeometric functions and modular forms (unabrigded version)
• Bivariate Extensions of Abramov's Algorithm for Rational Summation
• Residues and Telescopers for Rational Functions
• Diagonals of rational functions: from differential algebra to effective algebraic geometry (unabridged version)
• Reduction-Based Creative Telescoping for Algebraic Functions