International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 1, Pages 43-49
doi:10.1155/S0161171202108222
Application of uniform asymptotics to the fifth Painlevé transcendant
1Department of Mathematics and Computer Science, Bloomsburg University, Bloomsburg 17815, PA, USA
2Department of Mathematics, Millersville University, Millersville 17551-0302, PA, USA
Received 30 August 2001
Copyright © 2002 Youmin Lu and Zhoude Shao. 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.
Abstract
We apply the uniform asymptotics method to the fifth Painlevé transcendants, find its asymptotics of the form y=−1+t−1/2A(t) as t→∞ along the positive t-axis, and obtain the corresponding monodromy data.