Computation of Asymptotic Expansions of Turning Point Problems via Cauchy’s Integral Formula: Bessel Functions
| Autor: | Javier Segura, T. M. Dunster, Amparo Gil |
|---|---|
| Přispěvatelé: | Universidad de Cantabria |
| Rok vydání: | 2017 |
| Předmět: |
Asymptotic analysis
Series (mathematics) General Mathematics 010102 general mathematics Mathematical analysis Numerical Analysis (math.NA) 010103 numerical & computational mathematics 01 natural sciences Method of matched asymptotic expansions Computational Mathematics symbols.namesake Airy function Mathematics - Classical Analysis and ODEs 34E0 34E20 33C10 33F05 Classical Analysis and ODEs (math.CA) FOS: Mathematics symbols Mathematics - Numerical Analysis 0101 mathematics Asymptotic expansion Analysis Bessel function Cauchy's integral formula Mathematics Taylor expansions for the moments of functions of random variables |
| Zdroj: | Constr Approx (2017) 46:645?675 UCrea Repositorio Abierto de la Universidad de Cantabria Universidad de Cantabria (UC) |
| ISSN: | 1432-0940 0176-4276 |
| DOI: | 10.1007/s00365-017-9372-8 |
| Popis: | Linear second order differential equations having a large real parameter and turning point in the complex plane are considered. Classical asymptotic expansions for solutions involve the Airy function and its derivative, along with two infinite series, the coefficients of which are usually difficult to compute. By considering the series as asymptotic expansions for two explicitly defined analytic functions, Cauchy's integral formula is employed to compute the coefficient functions to high order of accuracy. The method employs a certain exponential form of Liouville-Green expansions for solutions of the differential equation, as well as for the Airy function. We illustrate the use of the method with the high accuracy computation of Airy-type expansions of Bessel functions of complex argument. Comment: To appear in Constructive Approximation |
| Databáze: | OpenAIRE |
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