Resurgence relation and global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach

A global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach is presented,with respect to the polynomial degree.The domains of uniformity are described in certain phase variables.A resurgence relation within the sequence of Riemann-Hilbert problems is observed in the procedure of derivation.Global asymptotic approximations are obtained in terms of the Airy function.The system of Hermite polynomials is used as an illustration.