On the structure of compatible rational functions

A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the structure of compatible rational functions. The theorem enables us to decompose a solution of such a system as a product of a rational function, several symbolic powers, a hyperexponential function, a hypergeometric term, and a q-hypergeometric term. We outline an algorithm for computing this product, and present an application. Categories and Subject Descriptors

• Type: Journal
• Year: 2011
• Where: ISSAC
• Authors: Shaoshi Chen, Ruyong Feng, Guofeng Fu, Ziming Li
• Keywords: Application Categories, ISSAC 2011, Mathematics, Rational Functions, Shift Operators