Linearization of Arbitrary products of classical orthogonal polynomials

Hounkonnou, Mahouton; Belmehdi, Said; Ronveaux, André

Hounkonnou, Mahouton ; Belmehdi, Said ; Ronveaux, André

Applicationes Mathematicae, Tome 27 (2000), p. 187-196 / Harvested from The Polish Digital Mathematics Library

Résumé

A procedure is proposed in order to expand $w = \prod_{j = 1}^{N} P_{i_{j}} (x) = \sum_{k = 0}^{M} L_{k} P_{k} (x)$ where $P_{i} (x)$ belongs to aclassical orthogonal polynomial sequence (Jacobi, Bessel, Laguerre and Hermite) ( $M = \sum_{j = 1}^{N} i_{j}$ ). We first derive a linear differential equation of order $2^{N}$ satisfied by w, fromwhich we deduce a recurrence relation in k for the linearizationcoefficients $L_{k}$ . We develop in detail the two cases ${[P_{i} (x)]}^{N}$ , $P_{i} (x) P_{j} (x) P_{k} (x)$ and give the recurrencerelation in some cases (N=3,4), when the polynomials $P_{i} (x)$ are monic Hermite orthogonal polynomials.

Publié le : 2000-01-01

Zbl 0997.33002

EUDML-ID : urn:eudml:doc:219266

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     author = {Mahouton Hounkonnou and Said Belmehdi and Andr\'e Ronveaux},
     title = {Linearization of Arbitrary products of classical orthogonal polynomials},
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     volume = {27},
     year = {2000},
     pages = {187-196},
     zbl = {0997.33002},
     language = {en},
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Hounkonnou, Mahouton; Belmehdi, Said; Ronveaux, André. Linearization of Arbitrary products of classical orthogonal polynomials. Applicationes Mathematicae, Tome 27 (2000) pp. 187-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv27i2p187bwm/

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