Bivariate Extensions of Abramov's Algorithm for Rational Summation

Abstract

Abramov's algorithm enables us to decide whether a univariate rational function can be written as a difference of another rational function, which has been a fundamental algorithm for rational summation. In 2014, Chen and Singer generalized Abramov's algorithm to the case of rational functions in two ($q$-)discrete variables. In this paper we solve the remaining three mixed cases, which completes our recent project on bivariate extensions of Abramov's algorithm for rational summation.

Dedicated to Professor Sergei A. Abramov on the occasion of his 70th birthday