Some results of ϖ-Painlevé difference equation

Abstract

Abstract In this article, we mainly investigate some properties of two types of difference equations Y(ϖz)+Y(z)+Y(zϖ)=ξz+oY(z)+v $$ Y(\varpi z)+Y(z)+Y\biggl(\frac{z}{\varpi}\biggr)=\frac{\xi z+o}{Y(z)}+v $$ and Y(ϖz)+Y(zϖ)=ξz+oY(z)+vY2(z). $$ Y(\varpi z)+Y\biggl(\frac{z}{\varpi}\biggr)=\frac{\xi z+o}{Y(z)}+ \frac{v}{Y^{2}(z)}. $$

Keywords

• Rational functions
• Complex difference equations
• Value distribution
• Finite order