Uniform asymptotic expansion of Charlier polynomials
نویسندگان
چکیده
منابع مشابه
Uniform Asymptotic Expansions for Charlier Polynomials
The asymptotic behaviour of the Charlier polynomials C (a) n (x) as nQ. is examined. These polynomials satisfy a discrete orthogonality relation and, unlike classical orthogonal polynomials, do not satisfy a second-order linear differential equation with respect to the independent variable x. As such, previous results on their asymptotic behaviour have been restricted to integral methods and co...
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Convergent expansions are derived for three types of orthogonal polynomials: Charlier, Laguerre and Jacobi. The expansions have asymptotic properties for large values of the degree. The expansions are given in terms of functions that are special cases of the given polynomials. The method is based on expanding integrals in one or two points of the complex plane, these points being saddle points ...
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We use the method of positive quadratic forms and discrete analogues of the Laguerre inequality recently obtained by the author, to give bounds on the zeros of the Charlier polynomials, which are uniform in all parameters involved.
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Using Casorati determinants of Charlier polynomials (ca n )n , we construct for each finite set F of positive integers a sequence of polynomials cF n , n ∈ σF , which are eigenfunctions of a second order difference operator, where σF is certain infinite set of nonnegative integers, σF ( N. For suitable finite sets F (we call them admissible sets), we prove that the polynomials cF n , n ∈ σF , a...
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ژورنال
عنوان ژورنال: Methods and Applications of Analysis
سال: 1994
ISSN: 1073-2772,1945-0001
DOI: 10.4310/maa.1994.v1.n3.a4