Orthogonal polynomials related to the oscillatory: Chebyshev weight function
نویسندگان
چکیده
منابع مشابه
Orthogonal Polynomials Related to the Oscillatory-chebyshev Weight Function
L(p) = ∫ 1 −1 p(x)x(1− x2)−1/2eiζxdx, ζ ∈ R. Since the weight function alternates in sign in the interval of orthogonality, the existence of orthogonal polynomials is not assured. A nonconstructive proof of the existence is given. The three-term recurrence relation for such polynomials is investigated and the asymptotic formulae for recursion coefficients are derived. AMS Mathematics Subject Cl...
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This is a continuation of our previous investigations on polynomials orthogonal with respect to the linear functional L : P → C, where L = ∫ 1 −1 p(x) dμ(x), dμ(x) = (1 − x2)λ−1/2 exp(iζx) dx, and P is a linear space of all algebraic polynomials. Here, we prove an extension of our previous existence theorem for rational λ ∈ (−1/2, 0], give some hypothesis on three-term recurrence coefficients, ...
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We consider polynomials pn(x) that are orthogonal with respect to the oscillatory weight w(x) = e on [−1, 1], where ω > 0 is a real parameter. A first analysis of pn(x) for large values of ω was carried out in [5], in connection with complex Gaussian quadrature rules with uniform good properties in ω. In this contribution we study the existence, asymptotic behavior and asymptotic distribution o...
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ژورنال
عنوان ژورنال: Bulletin: Classe des sciences mathematiques et natturalles
سال: 2005
ISSN: 0561-7332
DOI: 10.2298/bmat0530047m