Publications de l'Institut Mathematique 2008 Volume 84, Issue 98, Pages: 49-60
doi:10.2298/PIM0898049M
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Orthogonal polynomials for the oscillatory-Gegenbauer weight

Milovanović Gradimir V., Cvetković Aleksandar S., Marjanović Zvezdan M.

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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