A Uniform Asymptotic Expansion for Krawtchouk Polynomials
نویسندگان
چکیده
منابع مشابه
Asymptotic analysis of the Krawtchouk polynomials by the WKB method
We analyze the Krawtchouk polynomials Kn(x,N, p, q) asymptotically. We use singular perturbation methods to analyze them for N → ∞, with appropriate scalings of the two variables x and n. In particular, the WKB method and asymptotic matching are used. We obtain asymptotic approximations valid in the whole domain [0, N ] × [0, N ], involving some special functions. We give numerical examples sho...
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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...
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For the Hahn and Krawtchouk polynomials orthogonal on the set {0, . . . , N} new identities for the sum of squares are derived which generalize the trigonometric identity for the Chebyshev polynomials of the first and second kind. These results are applied in order to obtain conditions (on the degree of the polynomials) such that the polynomials are bounded (on the interval [0, N ]) by their va...
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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 Approximation Theory
سال: 2000
ISSN: 0021-9045
DOI: 10.1006/jath.2000.3474