Orthogonal polynomials and generalized Gauss-Rys quadrature formulae
Orthogonal polynomials and the corresponding quadrature formulas of Gaussian type with respect to the even weight function $\omega^{\lambda}(t;x)=\exp(-x t^2)(1-t^2)^{\lambda-1/2}$ on $(-1,1)$, with parameters $\lambda>-1/2$ and $x>0$, are considered. For $\lambda=1/2$ these quadrature ru...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2021-12-01
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| Series: | Kuwait Journal of Science |
| Subjects: | |
| Online Access: | https://journalskuwait.org/kjs/index.php/KJS/article/view/10665 |
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| Summary: | Orthogonal polynomials and the corresponding quadrature formulas of Gaussian type with respect to the even weight function
$\omega^{\lambda}(t;x)=\exp(-x t^2)(1-t^2)^{\lambda-1/2}$ on $(-1,1)$, with parameters $\lambda>-1/2$ and $x>0$, are considered.
For $\lambda=1/2$ these quadrature rules reduce to the so-called
Gauss-Rys quadrature formulas, which were investigated earlier by several authors, e.g., Dupuis, Rys, King (1976 and 1983), Sagar (1992), Schwenke (2014), Shizgal (2015), King (2016), Milovanovi\'c (2018), etc. In this generalized case
the method of modified moments is used, as well as a transformation of quadratures on $(-1, 1)$ with $N$ nodes to ones on $(0,1)$ with only $(N+1)/2$
nodes. Such an approach provides a stable and very efficient numerical construction.
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| ISSN: | 2307-4108 2307-4116 |