Title

Generalizations of chebyshev polynomials and polynomial mappings

Authors

Authors

Y. Chen; J. Griffin;M. E. H. Ismail

Comments

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Abbreviated Journal Title

Trans. Am. Math. Soc.

Keywords

SIEVED ORTHOGONAL POLYNOMIALS; INTERVALS; Mathematics

Abstract

In this paper we show how polynomial mappings of degree K from a union of disjoint intervals onto [-1, 1] generate a countable number of special cases of generalizations of Chebyshev polynomials. We also derive a new expression for these generalized Chebyshev polynomials for any genus g, from which the coefficients of x(n) can be found explicitly in terms of the branch points and the recurrence coefficients. We find that this representation is useful for specializing to polynomial mapping cases for small K where we will have explicit expressions for the recurrence coefficients in terms of the branch points. We study in detail certain special cases of the polynomials for small degree mappings and prove a theorem concerning the location of the zeroes of the polynomials. We also derive an explicit expression for the discriminant for the genus 1 case of our Chebyshev polynomials that is valid for any configuration of the branch point.

Journal Title

Transactions of the American Mathematical Society

Volume

359

Issue/Number

10

Publication Date

1-1-2007

Document Type

Article

Language

English

First Page

4787

Last Page

4828

WOS Identifier

WOS:000247469900010

ISSN

0002-9947

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