  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.
