Authors: Milovanović, Gradimir
Stanić, Marija P.
Tomović Mladenović, Tatjana V.
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Gaussian type quadrature rules related to the oscillatory modification of the generalized Laguerre weight functions
Journal: Journal of Computational and Applied Mathematics
Volume: 437
First page: 115476
Issue Date: 2024
Rank: ~M21
ISSN: 0377-0427
DOI: 10.1016/
In this paper we consider weighted integrals with respect to a modification of the generalized Laguerre weight functions wα(x)=xαe−x, α>−1, on (0,+∞) by the oscillatory factor exp(iζx), where ζ>0. For calculation of such integrals for analytic real-valued functions in D={z∈ℂ∣Rez≥0,Imz≥0} we construct polynomials orthogonal with respect to the linear functional L:P→ℂ, given by L[p]=∫0+∞p(x)wα(x)exp(iζx)dx, where P is a linear space of all algebraic polynomials, as well as the corresponding quadrature rules of Gaussian type. The existence of such orthogonal polynomials and the corresponding three-term recurrence relations are proved. A few numerical examples are presented, including computation of the Cauchy principal value integrals.
Keywords: Gaussian quadrature rule | Integration of highly oscillatory functions | Modified generalized Laguerre weight | Orthogonal polynomials | Three-term recurrence relations
Publisher: Elsevier

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