Difference Equation for Modifications of Meixner Polynomials
نویسندگان
چکیده
منابع مشابه
Meixner Polynomials and Random Partitions
The paper deals with a 3-parameter family of probability measures on the set of partitions, called the z-measures. The z-measures first emerged in connection with the problem of harmonic analysis on the infinite symmetric group. They are a special and distinguished case of Okounkov’s Schur measures. It is known that any Schur measure determines a determinantal point process on the 1-dimensional...
متن کاملZeros 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 کاملUniform Asymptotics of the Meixner Polynomials
Using the Deift-Zhou steepest descent method, we derive locally uniform asymptotic formulas for the Meixner polynomials. So far as we know, the asymptotic behavior in a neighborhood of the origin has not been studied before. To fill this gap, we should impose a Cauchy integral, which is the uniformly bounded solution to a scalar Riemann-Hilbert problem, and which converges exponentially fast (a...
متن کاملOn the zeros of Meixner polynomials
We investigate the zeros of a family of hypergeometric polynomials Mn(x;β, c) = (β)n 2F1(−n,−x;β; 1 − 1c ), n ∈ N, known as Meixner polynomials, that are orthogonal on (0,∞) with respect to a discrete measure for β > 0 and 0 < c < 1. When β = −N , N ∈ N and c = p p−1 , the polynomials Kn(x; p,N) = (−N)n 2F1(−n,−x;−N ; 1 p ), n = 0, 1, . . . N , 0 < p < 1 are referred to as Krawtchouk polynomial...
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
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1995
ISSN: 0022-247X
DOI: 10.1006/jmaa.1995.1297