Orthogonal polynomials for modified weight functions
نویسندگان
چکیده
منابع مشابه
Orthogonal polynomials for modified Gegenbauer weight and corresponding quadratures
In this paper we consider polynomials orthogonal with respect to the linear functional L : P → C, defined by L[p] = ∫ 1 −1 p(x)(1 − x 2)λ−1/2 exp(iζ x) dx, where P is a linear space of all algebraic polynomials, λ > −1/2 and ζ ∈ R. We prove the existence of such polynomials for some pairs of λ and ζ , give some their properties, and finally give an application to numerical integration of highly...
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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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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1992
ISSN: 0377-0427
DOI: 10.1016/0377-0427(92)90140-s