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/j.cam.2023.115476 | Abstract: | 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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