Extensions of Schur’s irreducibility results

We prove that the generalized Laguerre polynomials L n ( α ) ( x ) with 0 ≤ α ≤ 50 are irreducible except for finitely many pairs ( n , α ) and that these exceptions are necessary. In fact, it follows from a more general statement.

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Bibliographic Details
Published in:Indagationes mathematicae 2011-07, Vol.21 (1), p.87-105
Main Authors: Laishram, Shanta, Shorey, T.N.
Format: Article
Language:English
Subjects:
Irreducibility
Laguerre polynomials
Primes
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Description
Summary:We prove that the generalized Laguerre polynomials L n ( α ) ( x ) with 0 ≤ α ≤ 50 are irreducible except for finitely many pairs ( n , α ) and that these exceptions are necessary. In fact, it follows from a more general statement.
ISSN:0019-3577
1872-6100
DOI:10.1016/j.indag.2011.03.002