Khokhlov, V. I. Polynomials orthogonal with respect to the multinomial distribution and the factorial-power formalism. (English. Russian original) Zbl 1033.60009 Theory Probab. Appl. 46, No. 3, 529-536 (2001); translation from Teor. Veroyatn. Primen. 46, No. 3, 585-592 (2001). Summary: 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. Cited in 3 Documents MSC: 60E05 Probability distributions: general theory 05E35 Orthogonal polynomials (combinatorics) (MSC2000) Keywords:binomial distribution; Poisson distribution; multinomial distribution; Krawtchouk polynomials; Poisson-Charlier polynomials; factorial-power polynomials; polynomials orthogonal with respect to multinomial distribution; combinatorial identities; Lerch identity PDFBibTeX XMLCite \textit{V. I. Khokhlov}, Theory Probab. Appl. 46, No. 3, 529--536 (2001; Zbl 1033.60009); translation from Teor. Veroyatn. Primen. 46, No. 3, 585--592 (2001) Full Text: DOI