It is known that the asymptotics of Laguerre polynomials
(or Gegenbauer polynomials
) can be expressed in terms of Hermite polynomials for large values of the order parameter
). This paper gives a uniform approach, based on generating functions, to derive such asymptotic expressions, not only for these but also for other classes of orhogonal polynomials. The details are worked out for Gegenbauer, Laguerre, Jacobi and Tricomi-Carlitz polynomials. From these asymptotics, estimates for the zeros of the polynomials can be obtained in terms of the zeros of Hermite polynomials. Also this aspect is worked out for the above mentioned classes.