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
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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.References
- Ralph P. Boas Jr. and R. Creighton Buck, Polynomial expansions of analytic functions, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 19, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin, 1964. Second printing, corrected. MR 0162914, DOI 10.1007/978-3-662-25170-6
- James Ward Brown, On the Sheffer $A$-type of certain modified polynomial sets, Proc. Amer. Math. Soc. 23 (1969), 718–722. MR 247151, DOI 10.1090/S0002-9939-1969-0247151-5
- L. Carlitz, Some generating functions for Laguerre polynomials, Duke Math. J. 35 (1968), 825–827. MR 240351
- J. L. Goldberg, A note on polynomials generated by $A(t)\psi [xH(t)]$, Duke Math. J. 32 (1965), 643–651. MR 185158, DOI 10.1215/S0012-7094-65-03269-2
- Wilhelm Magnus, Fritz Oberhettinger, and Raj Pal Soni, Formulas and theorems for the special functions of mathematical physics, Third enlarged edition, Die Grundlehren der mathematischen Wissenschaften, Band 52, Springer-Verlag New York, Inc., New York, 1966. MR 0232968, DOI 10.1007/978-3-662-11761-3
- I. M. Sheffer, Some properties of polynomial sets of type zero, Duke Math. J. 5 (1939), 590–622. MR 81, DOI 10.1215/S0012-7094-39-00549-1
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