Title: Some elementary results concerning Pollaczek–Chebyshev polynomials
Abstract: The Pollaczek polynomials are considered in the case λ = 1. As the other two parameters (a and b) tend to zero, these polynomials tend to the Chebyshev polynomials of the second kind and hence we call them Pollaczek–Chebyshev polynomials of the second kind. A finite Green's function method yields an expression for the nth such polynomial in terms of those of lower order. Asymptotic expressions are obtained for the zeros of these polynomials closest to the endpoints of the interval of orthogonality. These expressions illustrate earlier general results on the zeros of Pollaczek polynomials.
Publication Year: 2006
Publication Date: 2006-06-27
Language: en
Type: article
Indexed In: ['crossref']
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