Publications de l'Institut Mathématique, Nouvelle Série Vol. 84(98), pp. 49–60 (2008) 

ORTHOGONAL POLYNOMIALS FOR THE OSCILLATORYGEGENBAUER WEIGHTGradimir V. Milovanovic, Aleksandar S. Cvetkovic, and Zvezdan M. MarjanovicElektronski fakultet, Nis, SerbiaAbstract: 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 $\mathcal{L}=\int_{1}^1 p(x) d\mu(x)$, $d\mu(x)=(1x^2)^{\lambda1/2} \exp(i\zeta x) dx$, 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 threeterm recurrence coefficients, and derive some differential relations for our orthogonal polynomials, including the second order differential equation. Classification (MSC2000): 30C10; 33C47 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 9 Dec 2008. This page was last modified: 12 Dec 2008.
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