Decomposition of Laguerre polynomials with respect to the cyclic group of order n

✍ Scribed by Youssèf Ben Cheikh

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 509 KB
• Volume: 99
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(98)00145-9

✦ Synopsis

Let n be an arbitrary positive integer, We decompose the Laguerre polynomials L(m ~) as the sum of n polynomials L~'"'k); mE~; k=O, 1 ..... n-1; defined by

In this paper, we establish the close relation between these components and the Brafman polynomials. The use of a technique described in an earlier work [2] leads us firstly to derive, from the basic identities and relations for L~ ), other analogous for L~ '''k) that turn out to be two integral representations, an operational representation, some generating functions defined by means of the generalized hyperbolic functions of order n and the hyper-Bessel functions, some finite sums including multiplication and addition formulas, a non standard (2n + 1)-term recurrence relation and a differential equation of order 2n. Secondly, to express some identities of L~ ) as functions of the polynomials ~mr{~' "' kt. Some particular properties of L~ "'°), the first component, will be pointed out. (~) 1998 Elsevier Science B.V. All rights reserved.