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.
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
@article{10_2298_PIM0898049M,
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 },
year = {2008},
volume = {_N_S_84},
number = {98},
doi = {10.2298/PIM0898049M},
zbl = {1249.30011},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0898049M/}
}
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%0 Journal Article %A Gradimir V. Milovanović %A Aleksandar S. Cvetković %A Zvezdan M. Marjanović %T Orthogonal Polynomials for the Oscillatory-gegenbauer Weight %J Publications de l'Institut Mathématique %D 2008 %P 49 %V _N_S_84 %N 98 %U http://geodesic.mathdoc.fr/articles/10.2298/PIM0898049M/ %R 10.2298/PIM0898049M %G en %F 10_2298_PIM0898049M
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