On the Summability of Bivariate Rational Functions

TL;DR

This paper develops criteria to determine when bivariate rational functions can be expressed as sums of differences, enabling the evaluation of double sums through single sums and special functions.

Contribution

It introduces new criteria for summability of bivariate rational functions and applies them to evaluate complex double sums.

Findings

Criteria for summability of bivariate rational functions

Reduction of double sums to single sums

Evaluation of sums using special functions

Abstract

We present criteria for deciding whether a bivariate rational function in two variables can be written as a sum of two (q-)differences of bivariate rational functions. Using these criteria, we show how certain double sums can be evaluated, first, in terms of single sums and, finally, in terms of values of special functions.