Asymptotic Behavior of the Modulus of the Kernel and Error Bounds of Anti-Gaussian Quadrature Formulas with Jacobi Weights

Ramon Orive (), Ljubica Mihić, Aleksandar Pejčev, Miroslav Pranić and Stefan Spalević
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Ramon Orive: Departamento Anáísis Matemático, Instituto de Matemáticas y Aplicaciones (IMAULL), University of La Laguna, 38200 La Laguna, Spain
Ljubica Mihić: School of Electrical and Computer Engineering, Academy of Technical and Art Applied Studies, Faculty of Information Technology and Engineering, University Union—Nikola Tesla, 11000 Belgrade, Serbia
Aleksandar Pejčev: Department of Mathematics, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia
Miroslav Pranić: Faculty of Mathematics, University of Banja Luka, Mladena Stojanovića 2, 78 000 Banja Luka, Bosnia and Herzegovina
Stefan Spalević: Department of Mathematics, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia

Mathematics, 2025, vol. 13, issue 12, 1-10

Abstract: In this paper, the remainder term of anti-Gaussian quadrature rules for analytic integrands with respect to Jacobi weight functions ω a , b ( x ) = ( 1 − x ) a ( 1 + x ) b , where a , b > − 1 , is analyzed, and sharp estimates of the error are provided. These kinds of quadrature formulas were introduced by D.P. Laurie and have been recently studied by M.M. Spalević for the case of Jacobi-type weight functions ω .

Keywords: anti-Gaussian quadrature rule; Jacobi weight functions; error bounds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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