Geodesic
Families of Euler-Maclaurin formulae for composite Gauss-Legendre and Lobatto quadratures
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 38 (2013), p. 63 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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Beside a short account on the Euler-Maclaurin formula, using a recent progress in variable-precision arithmetic and symbolic computation and the corresponding {c Mathematica} package {t Ort-ho-go-nal-Po-ly-no-mi-als} $[$Facta Univ. Ser. Math. Inform. {\bf19} $(2004)$, $17-36;$ Math. Balkanica {\bf 26} $(2012)$, $169-184]$, we obtain extensions of the Euler-Maclaurin formula for the composite (shifted) Gauss-Legendre formula, as well as for its Lobatto modification. Some special cases are also presented.
Classification : 65D30 65D32 40C15
Keywords: Gauss-Legendre quadrature, Lobatto quadrature, Euler-Maclaurin formulae, Bernoulli numbers, Bernoulli polynomials, orthogonal polynomials, quadrature sum, remainder term 
@article{BASS_2013_38_a4,
     author = {G. V. Milovanovi\'c},
     title = {Families of {Euler-Maclaurin} formulae for composite {Gauss-Legendre} and {Lobatto} quadratures},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {63 },
     year = {2013},
     volume = {38},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASS_2013_38_a4/}
}
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G. V. Milovanović. Families of Euler-Maclaurin formulae for composite Gauss-Legendre and Lobatto quadratures. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 38 (2013), p. 63 . http://geodesic.mathdoc.fr/item/BASS_2013_38_a4/