Index-dependent parameters of Laguerre and related polynomial sets.

Brown, J. W.; Goldberg, J. L.

doi:10.1090/S0002-9939-1970-0268428-1

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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