Orthogonal Polynomials for the Oscillatory-gegenbauer Weight
نویسندگان
چکیده
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, and derive some differential relations for our orthogonal polynomials, including the second order differential equation.
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تاریخ انتشار 2008