Functions of the second kind for classical polynomials

    Authors

    M. E. H. Ismail;Z. S. I. Mansour

    Comments

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

    Abbreviated Journal Title

    Adv. Appl. Math.

    Keywords

    Raising and lowering operators; Rodrigues formulas; Askey-Wilson; operator; Wilson operator; Jackson q-difference operator; Big and small; q-Jacobi polynomial; Al-Salam-Chihara polynomials; Indeterminate moment; problems; ORTHOGONAL POLYNOMIALS; DIFFERENCE-EQUATIONS; WILSON POLYNOMIALS; Mathematics, Applied

    Abstract

    We give new derivations of properties of the functions of the second kind of the Jacobi, little and big q-Jacobi polynomials, and the symmetric Al-Salam Chihara polynomials for q > 1. We also study the Askey Wilson functions and the Wilson functions of second kind. An integration by parts formula is derived for the Wilson operator in appropriate Hilbert space. In case of undetermined moment problem, we prove that the function of second kind depends on the measure. (C) 2013 Elsevier Inc. All rights reserved.

    Journal Title

    Advances in Applied Mathematics

    Volume

    54

    Publication Date

    1-1-2014

    Document Type

    Article

    Language

    English

    First Page

    66

    Last Page

    104

    WOS Identifier

    WOS:000332427700004

    ISSN

    0196-8858

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