Journal ArticleDOI
On the Asymptotics of the Meixner—Pollaczek Polynomials and Their Zeros
X. Li,Roderick Wong +1 more
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TLDR
In this article, an infinite asymptotic expansion for the Meixner-Pollaczek polynomials was derived, which holds uniformly for -M≤α≤ M, where M can be any positive number.Abstract:
An infinite asymptotic expansion is derived for the Meixner—Pollaczek polynomials M
n
(nα;δ, η) as n→∞ , which holds uniformly for -M≤α≤ M , where M can be any positive number. This expansion involves the parabolic cylinder function and its derivative. If α
n, s
denotes the s th zero of M
n
(nα;δ, η) , counted from the right, and if α˜
n,s
denotes its s th zero counted from the left, then for each fixed s , three-term asymptotic approximations are obtained for both α
n,s
and α˜
n,s
as n→∞ .read more
Citations
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Journal ArticleDOI
The Riemann-Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]
TL;DR: In this article, the authors consider polynomials that are orthogonal on [−1,1] with respect to a modified Jacobi weight (1− x ) α (1+ x ) β h (x ), with α, β >−1 and h real analytic and strictly positive on [ −1, 1].
Journal ArticleDOI
Large parameter cases of the Gauss hypergeometric function
TL;DR: In this article, the authors consider the asymptotic behavior of the Gauss hypergeometric function when several of the parameters a, b, c are large and indicate which cases are of interest for orthogonal polynomials (Jacobi, but also Meixner, Krawtchouk, etc.).
Journal ArticleDOI
Effects of a Herbal Complex Against Eimeria tenella Infection in Chickens
A. Du,Songhua Hu +1 more
TL;DR: The herbal complex used in this study was effective against E. tenella infection in chickens and the birds with medication had significantly higher body weight gains than birds without medication.
MonographDOI
Special Functions and Orthogonal Polynomials
Richard Beals,Roderick Wong +1 more
TL;DR: The subject of special functions is often presented as a collection of disparate results, rarely organized in a coherent way as discussed by the authors, and the authors of this book emphasize general principles that unify and demarcate the subjects of study.
Meixner-Pollaczek polynomials and the Heisenberg algebra
TL;DR: In this paper, an alternative proof is given for the connection between a system of continuous Hahn polynomials and identities for symmetric elements in the Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys. Rev. Lett. 56, 2445 (1986); J. Math. 28, 509 (1987)].
References
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Journal ArticleDOI
Handbook of Mathematical Functions
Reference BookDOI
Asymptotics and Special Functions
TL;DR: A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool as discussed by the authors, and it can be found in many libraries.
Book
Theory of Functions of a Complex Variable
TL;DR: In this paper, the Laurent series is used for expanding functions in Taylor series, and the calculus of residues is used to expand functions in Laurent series volumes II, III, and IV.
Book
Asymptotic Approximations of Integrals
TL;DR: The basic concepts of asymptotic expansions, Mellin transform techniques, and the distributional approach are explained.