Multivariable Meixner, Krawtchouk, and Meixner–Pollaczek polynomials
نویسندگان
چکیده
منابع مشابه
Zeros of Meixner and Krawtchouk polynomials
We investigate the zeros of a family of hypergeometric polynomials 2F1(−n,−x; a; t), n ∈ N that are known as the Meixner polynomials for certain values of the parameters a and t. When a = −N, N ∈ N and t = p , the polynomials Kn(x; p,N) = (−N)n2F1(−n,−x;−N; p ), n = 0, 1, . . .N, 0 < p < 1 are referred to as Krawtchouk polynomials. We prove results for the zero location of the orthogonal polyno...
متن کاملReal zeros of Meixner and Krawtchouk polynomials
We use a generalised Sturmian sequence argument and the discrete orthogonality of the Krawtchouk polynomials for certain parameter values to prove that all the zeros of Meixner polynomials are real and positive for parameter ranges where they are no longer orthogonal. AMS MOS Classification: 33C45, 34C10, 42C05
متن کاملA System of Multivariable Krawtchouk Polynomials and a Probabilistic Application
Abstract. The one variable Krawtchouk polynomials, a special case of the 2F1 function did appear in the spectral representation of the transition kernel for a Markov chain studied a long time ago by M. Hoare and M. Rahman. A multivariable extension of this Markov chain was considered in a later paper by these authors where a certain two variable extension of the F1 Appel function shows up in th...
متن کاملMore zeros of krawtchouk polynomials
Three theorems are given for the integral zeros of Krawtchouk polynomials. First, five new infinite families of integral zeros for the binary (q = 2) Krawtchouk polynomials are found. Next, a lower bound is given for the next integral zero for the degree four polynomial. Finally, three new infinite families in q are found for the degree three polynomials. The techniques used are from elementary...
متن کاملOn Krawtchouk polynomials
Krawtchouk polynomials play an important role in coding theory and are also useful in graph theory and number theory. Although the basic properties of these polynomials are known to some extent, there is, to my knowledge, no detailed development available. My aim in writing this article is to fill in this gap. Notation In the following we will use capital letters for (algebraic) polynomials, fo...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 1989
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.528507