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Volume :28 Issue : 2 2001      Add To Cart                                                                    Download

On the Chebyshev polynomials

Auther : LYUBOMIR BOYADJIEV* AND RUDOLF SCHERER**

*Universutat Karlsruhe (TH), Mathematisches Institut II, 76128 Karlsruhe, Germany
**Universitat (TH), Institut Praktische Mathematik, 76128 Karlsruhe, Germany
 
ABSTRACT
 
We put special attention in this paper on the Chebyshev polynomials of the fourth kind because they are much less known and less studied than others.  The representation problem of analytic functions in series of such polynomials is considered, and the importrant role of the Chebyshev functions of the second kind in solving them is emphasize.  For analytic functions, the remainder term of Gauss quadrature rules can be represented as a contour integral with a complex kernel function.  The kernel function related to the Gauss quadrature for Chebyshev polynomials of the fourth kind is especially studied on elliptic contours and the points of its maximum are specified.
 
Keywords:  Chebyshev polynomial; function of second kind; Gauss quadrature; quadrature error estimates; weries expansions.
 
MSC 2000: 05E35, 65D30

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