@Article{NMTMA-4-4,
author = {S., Cvetković, Aleksandar and Stanić, P., Marija and S., Cvetković, Aleksandar},
title = {Orthogonal Polynomials with Respect to Modified Jacobi Weight and Corresponding Quadrature Rules of Gaussian Type},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2011},
volume = {4},
number = {4},
pages = {478--488},
abstract = {<p style="text-align: justify;">In this paper we consider polynomials orthogonal with respect to the linear functional $\mathcal{L}:\mathcal{P}\to \mathbb{C}$, defined on the space of all algebraic polynomials $\mathcal{P}$ by$$\mathcal{L}[p] =\int_{-1}^1 p(x) (1-x)^{\alpha-1/2} (1+x)^{\beta-1/2}\exp(i\zeta x)dx,$$ where $\alpha,\beta &gt;-1/2$ are real numbers such that $\ell=|\beta-\alpha|$ is a positive integer, and
$\zeta\in\mathbb{R}\backslash\{0\}$. We prove the existence of such orthogonal polynomials for some pairs of $\alpha$ and $\zeta$ and for all nonnegative integers $\ell$. For such orthogonal polynomials we derive three-term recurrence relations and also some differential-difference relations. For such orthogonal polynomials the corresponding quadrature rules of Gaussian type are considered. &nbsp;Also, some numerical examples are included.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2011.m1039},
url = {https://global-sci.com/article/90707/orthogonal-polynomials-with-respect-to-modified-jacobi-weight-and-corresponding-quadrature-rules-of-gaussian-type}
}