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Uniform asymptotic expansions for the reverse generalized Bessel polynomials, and related functions. (English) Zbl 0983.33005
Generalized Bessel polynomials are considered for large degree. Uniform asymptotic expansions are derived by using Olver’s theory for second order linear differential equations. Two separate cases are considered, one for the case of complex domains which are free of turning points, and the other for complex domains containing a simple turning point (yielding Airy-type asymptotic expansions). Together the domains of validity cover the whole complex plane. The approximations are complete with explicit eror bounds. Other solutions of the differential equations are also considerd.

MSC:
33C15Confluent hypergeometric functions, Whittaker functions, 1 F 1
33C10Bessel and Airy functions, cylinder functions, 0 F 1
34E20Asymptotic singular perturbations, turning point theory, WKB methods (ODE)