Geodesic
Generalized Averaged Gaussian Formulas for Certain Weight Functions
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 2, p. 295 .

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In this paper we analyze the generalized averaged Gaussian quadrature formulas and the simplest truncated variant for one of them for some weight functions on the interval $[0,1]$ considered by Milovanović in \cite{grada}. We shall investigate internality of these formulas for the equivalents of the Jacobi polynomials on this interval and, in some special cases, show the existence of the Gauss-Kronrod quadrature formula. We also include some examples showing the corresponding error estimates for some non-classical orthogonal polynomials.
Classification : 65D30 65D32
Keywords: Gauss quadrature, Gauss-Kronrod quadrature, averaged Gaussian formulas, truncations of averaged Gaussian formulas 
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     author = {Rada M. Mutavd\v{z}i\'c},
     title = {Generalized {Averaged} {Gaussian} {Formulas} for {Certain} {Weight} {Functions}},
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Rada M. Mutavdžić. Generalized Averaged Gaussian Formulas for Certain Weight Functions. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 2, p. 295 . http://geodesic.mathdoc.fr/item/KJM_2022_46_2_a8/