Rational approximations of analytic functions

1990 ◽  
pp. 25-34 ◽  
Author(s):  
A. A. Gonchar
Keyword(s):  
Analytic Functions ◽  
Rational Approximations

On Padé and Best Rational Approximation

1983 ◽  
Vol 26 (1) ◽  
pp. 50-57 ◽  
Author(s):  
Peter B. Borwein
Keyword(s):  
Rational Approximation ◽  
Analytic Functions ◽  
Unit Disc ◽  
Padé Approximants ◽  
Main Diagonal ◽  
Rational Approximations ◽  
Pade Approximants ◽  
Best Rational Approximation

AbstractIt is reasonable to expect that, under suitable conditions, Padé approximants should provide nearly optimal rational approximations to analytic functions in the unit disc. This is shown to be the case for ez in the sense that main diagonal Padé approximants are shown to converge as expeditiously as best uniform approximants. Some more general but less precise related results are discussed.

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

Sign in / Sign up

Export Citation Format

Share Document