Zeros of Large Degree Vorob'ev–Yablonski Polynomials via a Hankel Determinant Identity.

In the present paper, we derive a new Hankel determinant representation for the square of the Vorob'ev-Yablonski polynomial Qn(x), x ϵ ℂ. These polynomials are the major ingredients in the construction of rational solutions to the second Painlevé equation uxx = xu+ 2u³ + α. As an application of the new identity, we study the zero distribution of Qn(x) as n→∞ by asymptotically analyzing a certain collection of (pseudo)- orthogonal polynomials connected to the aforementioned Hankel determinant. Our approach reproduces recently obtained results in the same context by Buckingham and Miller [3], which used the Jimbo-Miwa Lax representation of PII equation and the asymptotic analysis thereof. [ABSTRACT FROM AUTHOR]