Uniform asymptotic expansions for the reverse generalized Bessel polynomials, and related functions (Q2706221)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniform asymptotic expansions for the reverse generalized Bessel polynomials, and related functions |
scientific article |
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19 March 2001
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Bessel polynomials
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Liouville-Green expansions
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uniform asymptotic expansions
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turning point problems
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Uniform asymptotic expansions for the reverse generalized Bessel polynomials, and related functions (English)
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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.
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