On a class of q-orthogonal polynomials and the q-Riemann Hilbert Problem

Abstract

We give an explicit solution of a q-Riemann Hilbert problem which arises in the theory of orthogonal polynomials, prove that it is unique, and deduce several properties. Our new results include the asymptotic behaviour of zeroes in the limit as the degree of the polynomial approaches infinity.

arXiv comment15 pages, 1 figure

References in corpus (10)

• Quantum Inverse Scattering Method and Correlation Functions
• Exactly Solvable Birth and Death Processes
• Properties of Generalized Freud Polynomials
• Ladder Operators for q-orthogonal Polynomials
• Discrete quantum model of the harmonic oscillator
• Quantum state transfer in spin chains with q-deformed interaction terms
• Orthogonal Polynomials in Mathematical Physics
• A Generalised Sextic Freud Weight
• Zero distribution of orthogonal polynomials on a $q$-lattice
• The space of monodromy data for the Jimbo-Sakai family of $q$-difference equations

Cited by in corpus (5)

• On a class of elliptic orthogonal polynomials and their integrability
• Asymptotics of Discrete $q$-Freud $\mathrm{II}$ orthogonal polynomials from the $q$-Riemann Hilbert Problem
• Asymptotics for multiple q-orthogonal polynomials from the RHP
• Asymptotic behaviours of q-orthogonal polynomials from a q-Riemann Hilbert Problem
• $q$-deformation of random partitions, determinantal structure, and Riemann-Hilbert problem