On the asymptotics of Bessel functions in the Fresnel regime

DOI10.1016/j.acha.2014.12.002zbMath1321.33007arXiv1409.4100OpenAlexW2962813791MaRDI QIDQ2517413

James Bremer, Zhu Heitman, Bogdan Vioreanu, Vladimir Rokhlin

Publication date: 18 August 2015

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.4100

zbMATH Keywords

ordinary differential equationsspecial functionsphase functionsBessel's equation

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Numerical approximation and evaluation of special functions (33F05)

Related Items (12)

On computation of the Bessel function by summing up the series ⋮ An algorithm for the rapid numerical evaluation of Bessel functions of real orders and arguments ⋮ An algorithm for the numerical evaluation of the associated Legendre functions that runs in time independent of degree and order ⋮ On the existence of nonoscillatory phase functions for second order ordinary differential equations in the high-frequency regime ⋮ Error bounds for the large-argument asymptotic expansions of the Hankel and Bessel functions ⋮ Pólya's conjecture for Euclidean balls ⋮ On the Numerical Calculation of the Roots of Special Functions Satisfying Second Order Ordinary Differential Equations ⋮ On the numerical solution of second order ordinary differential equations in the high-frequency regime ⋮ Joint asymptotic expansions for Bessel functions ⋮ Asymptotic-numerical approximations for highly oscillatory second-order differential equations by the phase function method ⋮ Proofs of Two Conjectures on the Real Zeros of the Cylinder and Airy Functions ⋮ Improved estimates for nonoscillatory phase functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The ``phase function method to solve second-order asymptotically polynomial differential equations
• Bessel Functions for Large Arguments
• A Numerical Method for Evaluating Zeros of Solutions of Second-Order Linear Differential Equations

This page was built for publication: On the asymptotics of Bessel functions in the Fresnel regime