Orthogonal Polynomials for the Oscillatory-gegenbauer Weight
Publications de l'Institut Mathématique, (N.S.) 84 (2008) no. 98.

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This is a continuation of our previous investigations on polynomials orthogonal with respect to the linear functional $\mathcal{L}:\mathcal{P}\to\mathbb{C}$, where $\mathcal{L}=\int_{-1}^1 p(x)\,d\mu(x)$, $d\mu(x)=(1-x^2)^{\lambda-1/2} \exp(i\zeta x)\,dx$, and $\mathcal{P}$ is a linear space of all algebraic polynomials. Here, we prove an extension of our previous existence theorem for rational $\lambda\in(-1/2,0]$, 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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     author = {Gradimir V. Milovanovi\'c and Aleksandar S. Cvetkovi\'c and Zvezdan M. Marjanovi\'c},
     title = {Orthogonal {Polynomials} for the {Oscillatory-gegenbauer} {Weight}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {49 - 60},
     publisher = {mathdoc},
     volume = {(N.S.) 84},
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     year = {2008},
     zbl = {1249.30011},
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Gradimir V. Milovanović; Aleksandar S. Cvetković; Zvezdan M. Marjanović. Orthogonal Polynomials for the Oscillatory-gegenbauer Weight. Publications de l'Institut Mathématique, (N.S.) 84 (2008) no. 98. https://geodesic-test.mathdoc.fr/item/PIM_2008_N_S_84_98_a2/