0904.0640 (Qusay S. A. Al-Zamil)

Hankel Determinant structure of the Rational Solutions for Fifth
Painlevé Equation    [PDF]

Qusay S. A. Al-Zamil

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.

View original: http://arxiv.org/abs/0904.0640