Multiple orthogonal polynomials associated with an exponential cubic weight

Abstract

We consider multiple orthogonal polynomials associated with the exponential cubic weight e^{-x^3} over two contours in the complex plane. We study the basic properties of these polynomials, including the Rodrigues formula and nearest-neighbor recurrence relations. It turns out that the recurrence coefficients are related to a discrete Painlevé equation. The asymptotics of the recurrence coefficients, the ratio of the diagonal multiple orthogonal polynomials and the (scaled) zeros of these polynomials are also investigated.

23 pages, 7 figures

References in corpus (2)

• The nearest neighbor recurrence coefficients for multiple orthogonal polynomials
• Ladder operators and differential equations for multiple orthogonal polynomials

Cited by in corpus (7)

• Unique positive solution for an alternative discrete Painlevé I equation
• Critical measures for vector energy: global structure of trajectories of quadratic differentials
• Stokes Phenomena in Discrete Painlevé II
• Generalised Airy Polynomials
• Electrostatic partners and zeros of orthogonal and multiple orthogonal polynomials
• Large $z$ Asymptotics for Special Function Solutions of Painlevé II in the Complex Plane
• Nonlinear $q$-Stokes phenomena for $q$-Painlevé I