Hankel Determinant Structure of the Rational Solutions for Fifth Painlevé Equation

Qusay Soad Abdul-Aziz, Al-Zamil (2013) Hankel Determinant Structure of the Rational Solutions for Fifth Painlevé Equation. APPLIED MATHEMATICAL SCIENCES, Vol. 7 (No. 9). pp. 445-452. ISSN 1312-885X (print) ISSN 1314-7552 (online)

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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 $\sigma_{n}$ for $ n\geq 0$ 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.

Item Type:	Article
Uncontrolled Keywords:	Painlev\'{e} equations, Hankel determinant structure, Umemura polynomials.
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 34 Ordinary differential equations MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
Depositing User:	Mr. Qusay Soad Abdul-Aziz Al-Zamil
Date Deposited:	03 Feb 2014
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1256

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