Orthogonal polynomials and generalized Gauss-Rys quadrature formulae
Joint Authors
Milovanovic, Gradimir
Vasovic, Nevena
Source
Issue
Vol. 49, Issue 1 (31 Jan. 2022), pp.1-17, 17 p.
Publisher
Kuwait University Academic Publication Council
Publication Date
2022-01-31
Country of Publication
Kuwait
No. of Pages
17
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Milovanovic, Gradimir& Vasovic, Nevena. 2022. Orthogonal polynomials and generalized Gauss-Rys quadrature formulae. Kuwait Journal of Science،Vol. 49, no. 1, pp.1-17.
https://search.emarefa.net/detail/BIM-1500111
Modern Language Association (MLA)
Milovanovic, Gradimir& Vasovic, Nevena. Orthogonal polynomials and generalized Gauss-Rys quadrature formulae. Kuwait Journal of Science Vol. 49, no. 1 (Jan. 2022), pp.1-17.
https://search.emarefa.net/detail/BIM-1500111
American Medical Association (AMA)
Milovanovic, Gradimir& Vasovic, Nevena. Orthogonal polynomials and generalized Gauss-Rys quadrature formulae. Kuwait Journal of Science. 2022. Vol. 49, no. 1, pp.1-17.
https://search.emarefa.net/detail/BIM-1500111
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 16-17
Record ID
BIM-1500111