Geodesic
Polynomials Orthogonal with Respect to the Multinomial Distribution and the Factorial-Power Formalism
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 3, pp. 585-592

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A new combinatorial formalism is developed and applied to obtain new forms for Krawtchouk and Poisson–Charlier polynomials. These forms are used to obtain linear representations for pairwise products of such polynomials. As another application a family of polynomials orthogonal with respect to the multinomial distribution is established.
Mots-clés : binomial distribution, Poisson distribution, multinomial distribution, Krawtchouk polynomials, Poisson–Charlier polynomials
Keywords: factorial-power polynomials, polynomials orthogonal with respect to multinomial distribution, combinatorial identities, Lerch identity. 
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     author = {V. I. Khokhlov},
     title = {Polynomials {Orthogonal} with {Respect} to the {Multinomial} {Distribution} and the {Factorial-Power} {Formalism}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {585--592},
     publisher = {mathdoc},
     volume = {46},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_3_a14/}
}
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V. I. Khokhlov. Polynomials Orthogonal with Respect to the Multinomial Distribution and the Factorial-Power Formalism. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 3, pp. 585-592. http://geodesic.mathdoc.fr/item/TVP_2001_46_3_a14/