A moment problem and a family of integral evaluations

    Authors

    J. S. Christiansen;M. E. H. Ismail

    Comments

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    Abbreviated Journal Title

    Trans. Am. Math. Soc.

    Keywords

    indeterminate moment problems; q(-1)-hermite polynomials; Al-Salam-Chihara polynomials; biorthogonal rational functions; divided; difference operators; raising and lowering operators; Bethe Ansatz; equations; integral operators; CLASSICAL ORTHOGONAL POLYNOMIALS; ASKEY-WILSON OPERATOR; Q-HERMITE; POLYNOMIALS; Q-BETA-INTEGRALS; INVERSE; Mathematics

    Abstract

    We study the Al-Salam-Chihara polynomials when q > 1. Several solutions of the associated moment problem are found, and the orthogonality relations lead to explicit evaluations of several integrals. The polynomials are shown to have raising and lowering operators and a second order operator equation of Sturm-Liouville type whose eigenvalues are found explicitly. We also derive new measures with respect to which the Ismail-Masson system of rational functions is biorthogonal. An integral representation of the right inverse of a divided difference operator is also obtained.

    Journal Title

    Transactions of the American Mathematical Society

    Volume

    358

    Issue/Number

    9

    Publication Date

    1-1-2006

    Document Type

    Article

    Language

    English

    First Page

    4071

    Last Page

    4097

    WOS Identifier

    WOS:000238321800014

    ISSN

    0002-9947

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