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Generating functions for relatives of classical polynomials


Authors: P. D. Barry and D. J. Hurley
Journal: Proc. Amer. Math. Soc. 103 (1988), 839-846
MSC: Primary 33A99; Secondary 05A15
DOI: https://doi.org/10.1090/S0002-9939-1988-0947668-3
MathSciNet review: 947668
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Abstract: For several classical polynomials $ {u_n}(x)$ satisfying a second order linear differential equation $ {D_n}(x)$, there is a generating function $ u(x,t) = \sum\nolimits_{n = 0}^\infty {{u_n}(x){t^n}} $. We provide expansions $ \upsilon (x,t) = \sum\nolimits_{n = 0}^\infty {{\upsilon _n}(x){t^n}} $ where $ {\upsilon _n}(x)$ is a second solution of $ {D_n}(x)$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0947668-3
Keywords: Generating functions, classical polynomials, orthogonal polynomials
Article copyright: © Copyright 1988 American Mathematical Society

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