Zero distribution of sequences of classical orthogonal polynomials
نویسندگان
چکیده
منابع مشابه
Zero Distribution of Sequences of Classical Orthogonal Polynomials
In this paper, we study the zero distribution of sequences of Jacobi, Laguerre, and Hermite polynomials. Our approach is based on identifying these orthogonal polynomials with certain Fekete polynomials defined below, and using monotonicity properties of the zeros of the polynomials. Let E ⊂ R be a closed set that consists of finitely many intervals. Let w : E→ [0,∞) be a weight function such t...
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We use generating functions to express orthogonality relations in the form of q-beta integrals. The integrand of such a q-beta integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials of Szegő and leads naturally to the Al-Salam-Chihara p...
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Let x1 and xk be the least and the largest zeros of the Laguerre or Jacobi polynomial of degree k. We shall establish sharp inequalities of the form x1 < A, xk > B, which are uniform in all the parameters involved. Together with inequalities in the opposite direction, recently obtained by the author, this locates the extreme zeros of classical orthogonal polynomials with the relative precision,...
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2003
ISSN: 1085-3375,1687-0409
DOI: 10.1155/s1085337503306347