Accelerated polynomial approximation of finite order entire functions by growth reduction

DOI10.1090/S0025-5718-97-00832-6zbMath0864.65011OpenAlexW2012295246MaRDI QIDQ3127330

Jürgen Müller

Publication date: 8 April 1997

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-97-00832-6

zbMATH Keywords

numerical examplesconvergence accelerationpolynomial approximationBessel functionscomplex error functionfinite order entire functionsreduced growth method

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) 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) Representations of entire functions of one complex variable by series and integrals (30D10) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

Related Items (4)

A Jentzsch-theorem for Kapteyn, Neumann and general Dirichlet series ⋮ Accuracy and stability of computing high-order derivatives of analytic functions by Cauchy integrals ⋮ Generalized growth and best approximation of entire functions in \(L^p\) -norm in several complex variables ⋮ Linear semi-infinite programming theory: an updated survey

Uses Software

• Algorithm 413
• Algorithm 644
• Algorithm 680

Cites Work

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• Exceptional values of solutions of linear differential equations
• On two methods for accelerating convergence of series
• On the computation of incomplete gamma functions in the complex domain
• Accelerating the convergence of power series of certain entire functions
• On Faber polynomials and Faber expansions
• The degree of convergence for entire functions
• An Acceleration Method for the Power Series of Entire Functions of Order 1
• Near-Minimax Polynomial Approximation in an Elliptical Region
• Computation of Faber Series With Application to Numerical Polynomial Approximation in the Complex Plane
• Explicit Faber Polynomials on Circular Sectors
• The Faber Polynomials for Annular Sectors
• Erratum: Computation of the Complex Error Function
• Algorithm 680: evaluation of the complex error function
• Truncation Errors in Pade Approximations to Certain Functions: An Alternative Approach
• Efficient Computation of the Complex Error Function
• Approximation and interpolation of entire functions

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