Hermite polynomials are considered as approximants in asymptotic representations of certain other polynomials. Examples are given for polynomials from the Askey scheme of hypergeometric orthogonal polynomials. We also mention that Hermite polynomials can be used as main approximants in uniform asymptotic representations of certain types of integrals and differential equations.

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Temme, N.M, & López, J.L. (1999). The role of Hermite polynomials in asymptotic analysis. Modelling, Analysis and Simulation [MAS]. CWI.