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On a certain family of generalized Laguerre polynomials

✍ Scribed by Elizabeth A Sell

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
261 KB
Volume
107
Category
Article
ISSN
0022-314X

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✦ Synopsis

Following the work of Schur and Coleman, we prove the generalized Laguerre polynomial

x j is irreducible over the rationals for all nX1 and has Galois group A n if n þ 1 is an odd square, and S n otherwise. We also show that for certain negative integer values of a and certain congruence classes of n modulo 8, the splitting field of L ðaÞ n ðxÞ can be embedded in a double cover.

πŸ“œ SIMILAR VOLUMES

On Sobolev Orthogonality for the General
On Sobolev Orthogonality for the Generalized Laguerre Polynomials
✍ Teresa E. PΓ©rez; Miguel A. PiΓ±ar πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 359 KB

The orthogonality of the generalized Laguerre polynomials, [L (:) n (x)] n 0 , is a well known fact when the parameter : is a real number but not a negative integer. In fact, for &1<:, they are orthogonal on the interval [0, + ) with respect to the weight function \(x)=x : e &x , and for :<&1, but n