ON THE ATKIN POLYNOMIALS

    Authors

    A. El-Guindy;M. E. H. Ismail

    Comments

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    Abbreviated Journal Title

    Pac. J. Math.

    Keywords

    associated Jacobi polynomials; asymptotics; weight functions; scaled; invariant; modular function; birth and death process polynomials; supersingular polynomials; Hecke operators; Mathematics

    Abstract

    We identify the Atkin polynomials in terms of associated Jacobi polynomials. Our identification then takes advantage of the theory of orthogonal polynomials and their asymptotics to establish many new properties of the Atkin polynomials. This shows that corecursive polynomials may lead to interesting sets of orthogonal polynomials.

    Journal Title

    Pacific Journal of Mathematics

    Volume

    272

    Issue/Number

    1

    Publication Date

    1-1-2014

    Document Type

    Article

    Language

    English

    First Page

    111

    Last Page

    129

    WOS Identifier

    WOS:000346905600005

    ISSN

    0030-8730

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