Generalizations of chebyshev polynomials and polynomial mappings

    Authors

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

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    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

    Share

    COinS