×

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.

MSC:

60E05 Probability distributions: general theory
05E35 Orthogonal polynomials (combinatorics) (MSC2000)
PDFBibTeX XMLCite
Full Text: DOI