Expansions in the Askey-Wilson polynomials

    Authors

    M. E. H. Ismail;D. Stanton

    Comments

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    Abbreviated Journal Title

    J. Math. Anal. Appl.

    Keywords

    Andrews formula; Askey-Wilson polynomials; Basic hypergeometric series; Generating functions; Expansion formulas; INTEGRAL-OPERATORS; DIAGONALIZATION; Mathematics, Applied; Mathematics

    Abstract

    We give a general expansion formula of functions in the Askey-Wilson polynomials and using Askey-Wilson orthogonality we evaluate several integrals. Moreover we give a general expansion formula of functions in polynomials of Askey-Wilson type, which are not necessarily orthogonal. Limiting cases give expansions in little and big q-Jacobi type polynomials. We also give a new generating function for Askey-Wilson polynomials and a new evaluation for specialized Askey-Wilson polynomials. (C) 2014 Elsevier Inc. All rights reserved.

    Journal Title

    Journal of Mathematical Analysis and Applications

    Volume

    424

    Issue/Number

    1

    Publication Date

    1-1-2015

    Document Type

    Article

    Language

    English

    First Page

    664

    Last Page

    674

    WOS Identifier

    WOS:000348488700039

    ISSN

    0022-247X

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