Uniform Asymptotic Expansions for Charlier Polynomials

  title={Uniform Asymptotic Expansions for Charlier Polynomials},
  author={T. Mark Dunster},
  journal={Journal of Approximation Theory},
The asymptotic behaviour of the Charlier polynomials C (a) n (x) as nQ. is examined. These polynomials satisfy a discrete orthogonality relation and, unlike classical orthogonal polynomials, do not satisfy a second-order linear differential equation with respect to the independent variable x. As such, previous results on their asymptotic behaviour have been restricted to integral methods and consequently have been quite limited in their scope. In this paper a new approach is used, where the… CONTINUE READING