Zeros of orthogonal polynomials with respect to Bessel functions

PABLO ROMÁN

San Jose de Rio Preto

Workshop; Third Iberoamerican workshop on orthogonal polynomials and applications; 2013

In this talk I will discuss the asymptotic properties of a family of polynomials P_n(x) that are orthogonal with respect to Bessel functions J_nu(x), nu>0, on the positive real axis and I will describe the asymptotic zero distribution in the complex plane. These polynomials were introduced in [AH], in the context of complex Gaussian quadrature of integrals involving Bessel and other classical special functions. The asymptotic analysis is based on a steepest descent analysis of a Riemann-Hilbert problem.