Symbolic and numerical computation on Bessel functions of complex argument and large magnitude

DOI10.1016/S0377-0427(96)00063-5zbMath0865.65006OpenAlexW1977390864MaRDI QIDQ2564285

Jun Zhang

Publication date: 7 January 1997

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(96)00063-5

zbMATH Keywords

numerical experimentssymbolic computationBessel functionsFaber polynomialsChebyshev seriesHankel functionsLanczos tau methodcomplex argument

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Computation of special functions and constants, construction of tables (65D20) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items

On the best linear approximation of holomorphic functions ⋮ A note on the tau-method approximations for the Bessel functions \(Y_ 0(z)\) and \(Y_ 1(z)\) ⋮ Chebyshev series approximations for the Bessel function \(Y_n(z)\) of complex argument

Uses Software

• SPECFUN
• Algorithm 644

Cites Work

• On Clenshaw's method and a generalisation to Faber series
• Polynomial approximations in the complex plane
• Complex polynomial approximation by the Lanczos \(\tau\)-method: Dawson's integral
• On semiiterative methods generated by Faber polynomials
• Numerical evaluation of Airy functions with complex arguments
• Error analysis of the Tau method: Dependence of the approximation error on the choice of perturbation term
• Least squares data fitting using shape preserving piecewise approximations
• A hybrid Arnoldi-Faber iterative method for nonsymmetric systems of linear equations
• Tau-method approximations for the Bessel function \(Y_ 0 (z)\)
• Tau-method approximations for the Bessel function \(Y_ 1 (z)\)
• A note on the tau-method approximations for the Bessel functions \(Y_ 0(z)\) and \(Y_ 1(z)\)
• The special functions and their approximations. Vol. I, II
• Chebyshev Methods for Ordinary Differential Equations
• Computation of Faber Series With Application to Numerical Polynomial Approximation in the Complex Plane
• On the Faber Transform and Efficient Numerical Rational Approximation
• The Faber Polynomials for Circular Sectors
• The Faber polynomials for circular sectors
• Explicit Faber Polynomials on Circular Sectors
• A Faber Series Approach to Cardinal Interpolation
• Explicit Faber polynomials on circular sectors
• The Lanczos Tau-method
• Computation of the Complex Error Function
• Algorithm 715: SPECFUN–a portable FORTRAN package of special function routines and test drivers
• Algorithm 644
• Chebyshev Expansions for the Bessel Function J n (z) in the Complex Plane
• The Tau Method
• Faber Polynomials and the Faber Series
• Trigonometric Interpolation of Empirical and Analytical Functions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item