An update on orthogonal polynomials and weighted approximation on the real line

We briefly review the state of orthogonal polynomials on (–, ), concentrating on analytic aspects, such as asymptotics and bounds on orthogonal polynomials, their zeros and their recurrence coefficients. We emphasize results rather than proofs. We also discuss applications to mean convergence of orthogonal expansions, Lagrange interpolation, Jackson-Bernstein theorems and the weighted incomplete polynomial approximation problem.