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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Some polynomials defined by generating relations

Authors: H. M. Srivastava and R. G. Buschman
Journal: Trans. Amer. Math. Soc. 205 (1975), 360-370
MSC: Primary 33A70
Addendum: Trans. Amer. Math. Soc. 226 (1977), 393-394.
MathSciNet review: 0369770
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Abstract: In an attempt to present a unified treatment of the various polynomial systems introduced from time to time, new generating functions are given for the sets of polynomials $ \{ S_{n,q}^{(\alpha ,\beta )}(\lambda ;x)\} $ and $ \{ T_{n,q}^{(\alpha ,\beta )}(\lambda ;x)\} $, defined respectively by (6) and (29) below, and for their natural generalizations in several complex variables. This paper also indicates relevant connections of the results derived here with different classes of generating relations which have appeared recently in the literature.

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Keywords: Generating functions, polynomial systems, differential operator, Lagrange's expansion formula, special functions, Jacobi polynomials, Bessel polynomials, hypergeometric generating functions, pseudo Laguerre polynomials, multidimensional generating relations
Article copyright: © Copyright 1975 American Mathematical Society

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