Numerical calculation of Bessel, Hankel and Airy functions

DOI10.1016/j.cpc.2011.11.010zbMath1264.65028arXiv1112.0072OpenAlexW2078056344MaRDI QIDQ1948849

Ulrich D. Jentschura, E. Lötstedt

Publication date: 25 April 2013

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.0072

zbMATH Keywords

numerical examplesconvergence accelerationasymptotic expansionsBessel functionAiry functionssequence transformationssaddle point methodsHankel functionDebye polynomialsprinciple of asymptotic overlap

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Numerical approximation and evaluation of special functions (33F05)

Related Items (7)

On computation of the Bessel function by summing up the series ⋮ A hybrid approach to solve the high-frequency Helmholtz equation with source singularity in smooth heterogeneous media ⋮ Asymptotic approximations for solutions of Sturm-Liouville differential equations with a large complex parameter and nonsmooth coefficients ⋮ The resurgence properties of the large-order asymptotics of the Hankel and Bessel functions ⋮ On numerical evaluation of integrals involving oscillatory Bessel and Hankel functions ⋮ Computing Hypergeometric Functions Rigorously ⋮ Convergence analysis of the summation of the factorially divergent Euler series by Padé approximants and the delta transformation

Uses Software

• Mathematica
• Algorithm 838
• DLMF

Cites Work

• Summation of divergent power series by means of factorial series
• Convergence acceleration via combined nonlinear-condensation transformations
• Fast and accurate computation of Bessel functions with (large) complex order and argument
• An algorithm for the evaluation of the complex Airy functions
• On the evaluation of Bessel functions
• Numerical algorithms for uniform Airy-type asymptotic expansions
• Hyperasymptotic expansions of the modified Bessel function of the third kind of purely imaginary order
• An analysis of the impact of T. M. Cherry's work on asymptotic expansions
• On the Asymptotic Solutions of Ordinary Differential Equations, With an Application to the Bessel Functions of Large Order
• On the Asymptotic Solutions of Differential Equations, with an Application to the Bessel Functions of Large Complex Order
• On the use of Hadamard expansions in hyperasymptotic evaluation. II Complex variables
• On the use of Hadamard expansions in hyperasymptotic evaluation. I. Real variables
• Asymptotic expansion of the Dirac–Coulomb radial Green’s function
• On the resurgence properties of the uniform asymptotic expansion of Bessel functions of large order
• Numerical aspects of special functions
• Uniform asymptotic expansions of the modified Bessel function of the third kind of large imaginary order
• Numerical Methods for Special Functions
• Computation of complex Airy functions and their zeros using asymptotics and the differential equation
• Computational Aspects of Three-Term Recurrence Relations
• Recent Advances in Computational and Applied Mathematics
• Uniform Asymptotic Formulae for Functions with Transition Points
• ON THE CHOICE OF STANDARD SOLUTIONS FOR A HOMOGENEOUS LINEAR DIFFERENTIAL EQUATION OF THE SECOND ORDER
• The Asymptotic Solutions of Ordinary Linear Differential Equations of the Second Order, With Special Reference to a Turning Point
• Uniform Asymptotic Expansions
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