zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Asymptotic behaviors of intermediate points in the remainder of the Euler-Maclaurin formula. (English) Zbl 1207.65003
Summary: The Euler-Maclaurin formula is a very useful tool in calculus and numerical analysis. This paper is devoted to asymptotic expansion of the intermediate points in the remainder of the generalized Euler-Maclaurin formula when the length of the integral interval tends to be zero. In the special case we also obtain asymptotic behavior of the intermediate point in the remainder of the composite trapezoidal rule.

MSC:
65B15Euler-Maclaurin formula (numerical analysis)
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
41A55Approximate quadratures
41A80Remainders in approximation formulas
WorldCat.org
Full Text: DOI EuDML
References:
[1] G. Rzadkowski and S. Łepkowski, “A generalization of the Euler-Maclaurin summation formula: an application to numerical computation of the Fermi-Dirac integrals,” Journal of Scientific Computing, vol. 35, no. 1, pp. 63-74, 2008. · Zbl 1203.65013 · doi:10.1007/s10915-007-9175-3
[2] J.-P. Berrut, “A circular interpretation of the Euler-Maclaurin formula,” Journal of Computational and Applied Mathematics, vol. 189, no. 1-2, pp. 375-386, 2006. · Zbl 1086.65002 · doi:10.1016/j.cam.2005.02.015
[3] I. Franjić and J. Pe\vcarić, “Corrected Euler-Maclaurin’s formulae,” Rendiconti del Circolo Matematico di Palermo. Serie II, vol. 54, no. 2, pp. 259-272, 2005. · Zbl 1117.26016 · doi:10.1007/BF02874640
[4] L. Dedić, M. Matić, and J. Pe\vcarić, “Euler-Maclaurin formulae,” Mathematical Inequalities & Applications, vol. 6, no. 2, pp. 247-275, 2003. · Zbl 1036.26019
[5] D. Elliott, “The Euler-Maclaurin formula revisited,” Journal of Australian Mathematical Society Series B, vol. 40, pp. E27-E76, 1998/99. · Zbl 0928.65032
[6] F.-J. Sayas, “A generalized Euler-Maclaurin formula on triangles,” Journal of Computational and Applied Mathematics, vol. 93, no. 2, pp. 89-93, 1998. · Zbl 0938.65003 · doi:10.1016/S0377-0427(98)00049-1
[7] U. Abel, “On the Lagrange remainder of the Taylor formula,” American Mathematical Monthly, vol. 110, no. 7, pp. 627-633, 2003. · Zbl 1056.41026 · doi:10.2307/3647748
[8] U. Abel and M. Ivan, “The differential mean value of divided differences,” Journal of Mathematical Analysis and Applications, vol. 325, no. 1, pp. 560-570, 2007. · Zbl 1108.26006 · doi:10.1016/j.jmaa.2006.01.088
[9] B. Jacobson, “On the mean value theorem for integrals,” The American Mathematical Monthly, vol. 89, no. 5, pp. 300-301, 1982. · Zbl 0489.26003 · doi:10.2307/2321715
[10] B.-L. Zhang, “A note on the mean value theorem for integrals,” The American Mathematical Monthly, vol. 104, no. 6, pp. 561-562, 1997. · Zbl 0882.26001 · doi:10.2307/2975084
[11] W. J. Schwind, J. Ji, and D. E. Koditschek, “A physically motivated further note on the mean value theorem for integrals,” The American Mathematical Monthly, vol. 106, no. 6, pp. 559-564, 1999. · Zbl 0998.26004 · doi:10.2307/2589467
[12] R. C. Powers, T. Riedel, and P. K. Sahoo, “Limit properties of differential mean values,” Journal of Mathematical Analysis and Applications, vol. 227, no. 1, pp. 216-226, 1998. · Zbl 0923.26005 · doi:10.1006/jmaa.1998.6097
[13] T. Trif, “Asymptotic behavior of intermediate points in certain mean value theorems,” Journal of Mathematical Inequalities, vol. 2, no. 2, pp. 151-161, 2008. · Zbl 1169.26002
[14] A. M. Xu, F. Cui, and H. Z. Chen, “Asymptotic behavior of intermediate points in the differential mean value theorem of divided differences with repetitions,” Journal of Mathematical Analysis and Applications, vol. 365, no. 1, pp. 358-362, 2010. · Zbl 1252.26004 · doi:10.1016/j.jmaa.2009.10.067
[15] L. Comtet, Advanced Combinatorics, D. Reidel, Dordrecht, The Netherlands, 1974.