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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Index-dependent parameters of Laguerre and related polynomial sets.
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by J. W. Brown and J. L. Goldberg
Proc. Amer. Math. Soc. 25 (1970), 852-855
DOI: https://doi.org/10.1090/S0002-9939-1970-0268428-1

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.
References
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Bibliographic Information
  • © Copyright 1970 American Mathematical Society
  • 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