5 papers · 1 filter
Asymptotics of Polynomials Orthogonal With Respect to a Generalized Freud Weight With Application to Special Function Solutions of Painlevé-IV
Ahmad Barhoumi
We obtain asymptotics of polynomials satisfying the orthogonality relations $$ \int_{\mathbb{R}} z^k P_n(z; t , N) \mathrm{e}^{-N \left(\frac{1}{4}z^4 + \frac{t}{2}z^2 \right)} \ma…
Painlevé-III Monodromy Maps Under the Confluence and Applications to the Large-Parameter Asymptotics of Rational Solutions
Ahmad Barhoumi, Oleg Lisovyy, Peter D. Miller +1
The third Painlevé equation in its generic form, often referred to as Painlevé-III(), is given by $$ \frac{{\rm d}^2u}{{\rm d}x^2} =\frac{1}{u}\left(\frac{{\rm d}u}{{\rm d}x}\…
Non-Hermitian Orthogonal Polynomials on a Trefoil
Ahmad B. Barhoumi, Maxim L. Yattselev
We investigate asymptotic behavior of polynomials satisfying non-Hermitian orthogonality relations where …
Global Phase Portrait and Large Degree Asymptotics for the Kissing Polynomials
Ahmad Barhoumi, Andrew F. Celsus, Alfredo Deaño
We study a family of monic orthogonal polynomials which are orthogonal with respect to the varying, complex valued weight function, , over the interval , where $…
Asymptotics of Polynomials Orthogonal on a Cross with a Jacobi-type Weight
Ahmad Barhoumi, Maxim L. Yattselev
We investigate asymptotic behavior of polynomials satisfying non-Hermitian orthogonality relations $$ \int_Δs^kQ_n(s)ρ(s)\dd s =0, \quad k\in\{0,\ldots,n-1\}, $$ where $…