Qusay Soad Abdul-Aziz, Al-Zamil
(2013)
*Hankel Determinant Structure of the Rational Solutions for Fifth PainlevÃ© 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 |
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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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