ADDITION THEOREMS VIA CONTINUED FRACTIONS

    Authors

    M. E. H. Ismail;J. Zeng

    Comments

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    Abbreviated Journal Title

    Trans. Am. Math. Soc.

    Keywords

    Addition theorems; orthogonal polynomials; continued J-fractions; q-orthogonal polynomials; Askey-Wilson polynomials; Bessel and confluent; hypergeometric functions; HANKEL DETERMINANTS; POLYNOMIALS; Mathematics

    Abstract

    We show connections between a special type of addition formulas and a theorem of Stieltjes and Rogers. We use different techniques to derive the desirable addition formulas. We apply our approach to derive special addition theorems for Bessel functions and confluent hypergeometric functions. We also derive several addition theorems for basic hypergeometric functions. Applications to the evaluation of Hankel determinants are also given.

    Journal Title

    Transactions of the American Mathematical Society

    Volume

    362

    Issue/Number

    2

    Publication Date

    1-1-2010

    Document Type

    Article

    Language

    English

    First Page

    957

    Last Page

    983

    WOS Identifier

    WOS:000274739600016

    ISSN

    0002-9947

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