Computation of asymptotic expansions of turning point problems via Cauchy's integral formula: Bessel functions

DOI10.1007/s00365-017-9372-8zbMath1386.34107arXiv1607.08269OpenAlexW2591436796MaRDI QIDQ1691438

T. M. Dunster, Amparo Gil, Javier Segura

Publication date: 16 January 2018

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.08269

zbMATH Keywords

asymptotic expansionsnumerical computationBessel functionsturning point problems

Mathematics Subject Classification ID

Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Asymptotic expansions of solutions to ordinary differential equations (34E05) Numerical approximation and evaluation of special functions (33F05) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items (11)

Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions ⋮ Sharp error bounds for turning point expansions ⋮ Uniform asymptotic expansions for Lommel, Anger‐Weber, and Struve functions ⋮ Uniform asymptotic expansions for Gegenbauer polynomials and related functions via differential equations having a simple pole ⋮ Computation of parabolic cylinder functions having complex argument ⋮ Asymptotic approximations for solutions of Sturm-Liouville differential equations with a large complex parameter and nonsmooth coefficients ⋮ Asymptotic expansions relating to the distribution of the length of longest increasing subsequences ⋮ Simplified error bounds for turning point expansions ⋮ Liouville-Green expansions of exponential form, with an application to modified Bessel functions ⋮ Numerical evaluation of Airy-type integrals arising in uniform asymptotic analysis ⋮ Uniform asymptotic expansions for solutions of the parabolic cylinder and Weber equations

Uses Software

• Algorithm 838
• AIZ
• BIZ
• DLMF
• Algorithm 644
• IBESS JBESS

Cites Work

• Unnamed Item
• Accuracy and stability of computing high-order derivatives of analytic functions by Cauchy integrals
• Asymptotics of the eigenvalues of the rotating harmonic oscillator
• Numerical algorithms for uniform Airy-type asymptotic expansions
• CDC 6600 Subroutines IBESS and JBESS for Bessel Functions I _υ (x) and J _υ (x), x≥0,υ≥0
• Algorithm 644
• Asymptotic expansions for the coefficient functions that arise in turning-point problems
• Numerical Methods for Special Functions
• Algorithm 819: AIZ, BIZ
• Algorithm 838

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