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Zbl 0983.33005
Dunster, T.M.
Uniform asymptotic expansions for the reverse generalized Bessel polynomials, and related functions. (English)
[J] SIAM J. Math. Anal. 32, No.5, 987-1013 (2001). ISSN 0036-1410; ISSN 1095-7154/e

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.
[N.M.Temme (Amsterdam)]

MSC 2000:: *33C15 Confluent hypergeometric functions
33C10 Cylinder functions, etc.
34E20 Asymptotic singular perturbations, methods (ODE)

Keywords: Bessel polynomials; Liouville-Green expansions; uniform asymptotic expansions; turning point problems

Cited in: Zbl 1213.33011

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