A concise expression for the ODE's of orthogonal polynomials

Abstract

It is known that orthogonal polynomials obey a 3 terms recursion relation, as well as a 2x2 differential system. Here, we give an explicit and concise expression of the differential system in terms of the recursion coefficients. This result is a generalization of an expression of Fokas, Its and Kitaev for the symmetric case.

References in corpus (3)

• Random Matrix Theories in Quantum Physics: Common Concepts
• 2D Gravity and Random Matrices
• Fredholm Determinants, Differential Equations and Matrix Models

Cited by in corpus (6)

• Lectures on random matrix models. The Riemann-Hilbert approach
• Generalized Christoffel-Darboux formula for skew-orthogonal polynomials and random matrix theory
• Skew-orthogonal polynomials, differential systems and random matrix theory
• Asymptotics of the partition function of a random matrix model
• Critical asymptotic behavior for the Korteweg-de Vries equation and in random matrix theory
• Generalized Christoffel-Darboux formula for classical skew-orthogonal polynomials