Jacobi polynomials from compatibility conditions

    Authors

    Y. Chen;M. Ismail

    Comments

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    Abbreviated Journal Title

    Proc. Amer. Math. Soc.

    Keywords

    ORTHOGONAL POLYNOMIALS; FREUD POLYNOMIALS; Mathematics, Applied; Mathematics

    Abstract

    We revisit the ladder operators for orthogonal polynomials and re-interpret two supplementary conditions as compatibility conditions of two linear over-determined systems; one involves the variation of the polynomials with respect to the variable z ( spectral parameter) and the other a recurrence relation in n ( the lattice variable). For the Jacobi weight w(x) = (1-x)(alpha) (1+x)beta, x is an element of [-1, 1], we show how to use the compatibility conditions to explicitly determine the recurrence coefficients of the monic Jacobi polynomials.

    Journal Title

    Proceedings of the American Mathematical Society

    Volume

    133

    Issue/Number

    2

    Publication Date

    1-1-2005

    Document Type

    Article

    Language

    English

    First Page

    465

    Last Page

    472

    WOS Identifier

    WOS:000224695400020

    ISSN

    0002-9939

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