Geodesic
Orthogonal Polynomials for the Oscillatory-gegenbauer Weight
Publications de l'Institut Mathématique, _N_S_84 (2008) no. 98, p. 49 .

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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.
DOI : 10.2298/PIM0898049M
Classification : 30C10 33C47 
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     title = {Orthogonal {Polynomials} for the {Oscillatory-gegenbauer} {Weight}},
     journal = {Publications de l'Institut Math\'ematique},
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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, p. 49 . doi : 10.2298/PIM0898049M. http://geodesic.mathdoc.fr/articles/10.2298/PIM0898049M/

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