Geodesic
Multivariate Meixner, Charlier and Krawtchouk Polynomials According to Analysis on Symmetric Cones
Genki Shibukawa1
1Dept. of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
Journal of Lie Theory, Tome 26 (2016) no. 2, pp. 439-477

Voir la notice de l'article provenant de la source Heldermann Verlag

We introduce some multivariate analogues of Meixner, Charlier and Krawtchouk polynomials, and establish their main properties by using analysis on symmetric cones, that is, duality, degenerate limits, generating functions, orthogonality relations, difference equations, recurrence formulas and determinant expressions. A particularly important and interesting result is that "the generating function of the generating functions" for the Meixner polynomials coincides with the generating function of the Laguerre polynomials, which has previously not been known even for the one variable case. Actually, main properties for the multivariate Meixner, Charlier and Krawtchouk polynomials are derived from some properties of the multivariate Laguerre polynomials by using this key result.
Classification : 32M15, 33C45, 43A90
Mots-clés : Multivariate analysis, discrete orthogonal polynomials, symmetric cones, spherical polynomials, generalized binomial coefficients

Genki Shibukawa  1

1 Dept. of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan 
Genki Shibukawa. Multivariate Meixner, Charlier and Krawtchouk Polynomials According to Analysis on Symmetric Cones. Journal of Lie Theory, Tome 26 (2016) no. 2, pp. 439-477. http://geodesic.mathdoc.fr/item/JOLT_2016_26_2_a4/
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     author = {Genki Shibukawa},
     title = {Multivariate {Meixner,} {Charlier} and {Krawtchouk} {Polynomials} {According} to {Analysis} on {Symmetric} {Cones}},
     journal = {Journal of Lie Theory},
     pages = {439--477},
     year = {2016},
     volume = {26},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2016_26_2_a4/}
}
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