Hankel Determinant structure of the Rational Solutions for Fifth Painlev\'{e} Equation
Analysis of PDEs
2012-12-11 v3 Mathematical Physics
math.MP
Abstract
In this paper, we construct the Hankel determinant representation of the rational solutions for the fifth Painlev\'{e} equation through the Umemura polynomials. Our construction gives an explicit form of the Umemura polynomials for in terms of the Hankel Determinant formula. Besides, We compute the generating function of the entries in terms of logarithmic derivative of the Heun Confluent Function.
Cite
@article{arxiv.0904.0640,
title = {Hankel Determinant structure of the Rational Solutions for Fifth Painlev\'{e} Equation},
author = {Qusay S. A. Al-Zamil},
journal= {arXiv preprint arXiv:0904.0640},
year = {2012}
}
Comments
This paper has been published in Applied Mathematical Sciences, Vol. 7, 2013, no. 9, 445 - 452. Please, you can use the following link to get it http://www.m-hikari.com/ams/ams-2013/ams-9-12-2013/alzamilAMS9-12-2013.pdf