International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 13, Pages 845-851

On the asymptotic representation of the solutions to the fourth general Painlevé equation

Youmin Lu

Department of Mathematics, Computer Science and Statistics, College of Science and Technology, Bloomsburg University of Pennsylvania, Bloomsburg 17815, PA, USA

Received 5 June 2002

Copyright © 2003 Youmin Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


There have been many results on the asymptotics of the Painlevé transcendents in recent years, but the asymptotics of the fourth Painlevé transcendent has not been studied much. In this note, we study the general fourth Painlevé equation and develop an asymptotic representation of a group of its solutions as the independent variable approaches infinity along a straight line.