Orthogonal Polynomials for the Oscillatory-gegenbauer Weight
Publications de l'Institut Mathématique, (N.S.) 84 (2008) no. 98.
Voir la notice de l'article dans eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
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.
@article{PIM_2008_N_S_84_98_a2, 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}, number = {98}, year = {2008}, zbl = {1249.30011}, url = {https://geodesic-test.mathdoc.fr/item/PIM_2008_N_S_84_98_a2/} }
TY - JOUR AU - Gradimir V. Milovanović AU - Aleksandar S. Cvetković AU - Zvezdan M. Marjanović TI - Orthogonal Polynomials for the Oscillatory-gegenbauer Weight JO - Publications de l'Institut Mathématique PY - 2008 SP - 49 EP - 60 VL - (N.S.) 84 IS - 98 PB - mathdoc UR - https://geodesic-test.mathdoc.fr/item/PIM_2008_N_S_84_98_a2/ ID - PIM_2008_N_S_84_98_a2 ER -
%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 - 60 %V (N.S.) 84 %N 98 %I mathdoc %U https://geodesic-test.mathdoc.fr/item/PIM_2008_N_S_84_98_a2/ %F PIM_2008_N_S_84_98_a2
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/