An extremal problem and an estimation of the Wronskian of certain Jacobi polynomials

    Authors

    X. Li

    Comments

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    Abbreviated Journal Title

    J. Comput. Appl. Math.

    Keywords

    Jacobi polynomials; extremal problem; maximum; Wronskian; Mathematics, Applied

    Abstract

    We study an extremal problem related to "splitted" Jacobi weights: for alpha, beta > 0, find the largest value of max(xis an element of[-1,1]) [(1 + x)(beta) p(m)(x)(2) + (1 - x)(alpha)q(n)(x)(2)] among all polynomials p(m) and q(n) of degree at most m and n, respectively, satisfying integral(-1)(1) [(1 + x)(beta) p(m)(x)(2) + (1 - x)(alpha)q(n)(x)(2)] dx = 1. We show that the solution of this problem is related to an estimation of the Christoffel functions and the Wronskians associated with certain Jacobi polynomials. (C) 2002 Elsevier Science B.V. All rights reserved.

    Journal Title

    Journal of Computational and Applied Mathematics

    Volume

    153

    Issue/Number

    1-2

    Publication Date

    1-1-2003

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    311

    Last Page

    320

    WOS Identifier

    WOS:000181888700030

    ISSN

    0377-0427

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