Complex polynomial approximation by the Lanczos \(\tau\)-method: Dawson's integral

DOI10.1016/0377-0427(87)90131-2zbMath0639.65011OpenAlexW2087268288MaRDI QIDQ1099922

John P. Coleman

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0377-0427(87)90131-2

zbMATH Keywords

polynomial approximationFaber polynomialsFaber seriescomplex approximationtau-methodDawson's integral

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

Related Items (6)

Tau-method approximations for the Bessel function \(Y_ 0 (z)\) ⋮ An exponential Chebyshev second kind approximation for solving high-order ordinary differential equations in unbounded domains, with application to Dawson's integral ⋮ A note on the tau-method approximations for the Bessel functions \(Y_ 0(z)\) and \(Y_ 1(z)\) ⋮ The Faber Polynomials for Annular Sectors ⋮ Evaluating of Dawson's integral by solving its differential equation using orthogonal rational Chebyshev functions ⋮ Symbolic and numerical computation on Bessel functions of complex argument and large magnitude

Cites Work

• Numerical solution of nonlinear partial differential equations with the Tau method
• On Clenshaw's method and a generalisation to Faber series
• Polynomial approximations in the complex plane
• Near-circularity of the error curve in complex Chebyshev approximation
• Some remarks on uniform asymptotic expansions for Bessel functions
• Über die Faberschen Polynome schlichter Funktionen
• 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
• The Faber Polynomials for Circular Sectors
• The Lanczos Tau-method
• Exapansions of Dawson's Function in a Series of Chebyshev Polynomials
• The Tau Method
• Trigonometric Interpolation of Empirical and Analytical Functions
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