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Proceedings of the American Mathematical Society

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Index-dependent parameters of Laguerre and related polynomial sets.


Authors: J. W. Brown and J. L. Goldberg
Journal: Proc. Amer. Math. Soc. 25 (1970), 852-855
MSC: Primary 33.40
DOI: https://doi.org/10.1090/S0002-9939-1970-0268428-1
MathSciNet review: 0268428
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Abstract: It is known that linearity of the function $ \gamma (n)$ is sufficient for the set $ \{ L_n^{(\gamma (n))}(x)\} $ of generalized Laguerre polynomials to be of type zero as defined by I. M. Sheffer. We prove here that linearity is also necessary. This result is exhibited as a special case in the broader context of generalized Appell representations introduced by R. P. Boas, Jr. and R. C. Buck.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0268428-1
Keywords: Generalized Appell representation, Laguerre polynomials, zero type sets
Article copyright: © Copyright 1970 American Mathematical Society