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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



An equivalence theorem on generating functions

Author: H. M. Srivastava
Journal: Proc. Amer. Math. Soc. 52 (1975), 159-165
MSC: Primary 33A70
MathSciNet review: 0379931
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Abstract: The present paper establishes an equivalence theorem on generating relations for a sequence of functions $\{ {f_n}(z)\}$ defined by the Rodrigues formula (1) below. It is also shown how this theorem may be applied to a fairly large variety of special functions including, for instance, the classical orthogonal polynomials.

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Keywords: Equivalence theorem, generating relations, Rodrigues’ formula, special functions, classical orthogonal polynomials, holomorphic functions, the Cauchy-Hadamard theorem, d’Alembert’s ratio test, Cauchy’s integral formula, uniform convergence, binomial theorem, analytic continuation, Hermite polynomials, Laguerre polynomials, Jacobi polynomials, Bessel polynomials, ultraspherical polynomials, Legendre polynomials, Tchebycheff polynomials, Charlier polynomials, generating-function equivalence, Meixner polynomials
Article copyright: © Copyright 1975 American Mathematical Society