Geodesic
On some special polynomials and functions
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 205-226

Voir la notice de l'article provenant de la source Math-Net.Ru

A full system of homogeneous harmonic polynomials on $n$ variables is constructed. It is orthogonal in two spaces. On the base of these polynomials a notion of $G$-functions is introduced. Connections of $G$-functions with Legendre polynomials and Chebyshev polynomials are obtained and a Rodrigues formula is proved.
Keywords: harmonic polynomials, Legendre and Chebyshev polynomials, Gegenbauer's polynomials
Mots-clés : Rodrigues formula. 
@article{SEMR_2013_10_a58,
     author = {V. V. Karachik},
     title = {On some special polynomials and functions},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {205--226},
     publisher = {mathdoc},
     volume = {10},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a58/}
}
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V. V. Karachik. On some special polynomials and functions. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 205-226. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a58/