The Combinatorics of Meixner Polynomials: Linearization Coefficients

Abstract We describe various aspects of the Meixner polynomials. These include combinatorial descriptions of the moments, the orthogonality relation, and the linearization coefficients.

[1]  François Bergeron Combinatorics of classic orthogonal polynomials: a unified approach , 1990 .

[2]  Yeong-Nan Yeh,et al.  Combinatorial proofs of some limit formulas involving orthogonal polynomials , 1990, Discret. Math..

[3]  Jiang Zeng,et al.  The q -Stirling numbers, continued fractions and the q -Charlier and q -Laguerre polynomials , 1995 .

[4]  Doron Zeilberger,et al.  Laguerre Polynomials, Weighted Derangements, and Positivity , 1988, SIAM J. Discret. Math..

[5]  Gérard Viennot,et al.  The Combinatorics of q-Hermite polynomials and the Askey - Wilson Integral , 1987, Eur. J. Comb..

[6]  Yeong-Nan Yeh,et al.  Some Combinatorics of the Hypergeometric Series , 1988, Eur. J. Comb..

[7]  X. G. Viennot,et al.  Moments des q-Polynômes de Laguerre et la Bijection de Foata-Zeilberger , 1994 .

[8]  I. G. MacDonald,et al.  Symmetric functions and Hall polynomials , 1979 .

[9]  D. Foata La série génératrice exponentielle dans les problèmes d'énumération , 1974 .

[10]  Gérard Viennot,et al.  Combinatorial interpretation of integrals of products of hermite, Laguerre and Tchebycheff polynomials , 1985 .

[11]  Rodica Simion,et al.  Specializations of generalized Laguerre polynomials , 1993 .

[12]  Jiang Zeng Linearization of Meixner, Krawtchouk, and Charlier polynomial products , 1990 .

[13]  Dennis E. White,et al.  The Combinatorics of q-Charlier Polynomials , 1993, J. Comb. Theory, Ser. A.

[14]  Jiang Zeng,et al.  Weighted Derangements and the Linearization Coefficients of Orthogonal Sheffer Polynomials , 1992 .

[15]  T. Chihara,et al.  An Introduction to Orthogonal Polynomials , 1979 .