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

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
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/
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     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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