Abstract
The aim of this paper is to derive corrected Euler-Maclaurin’s formulae, i.e. open type quadrature formulae where the integral is approximated not only with the values of the function in points (5a+b)/6, (a+b)/2 and (a+5b)/6, but also with values of the first derivative in end points of the interval. These formulae will have a higher degree of exactness than the ones obtained in [2]. Using the derived formulae, a number of inequalities for various classes of functions are obtained.
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Franjić, I., Pečarić, J. Corrected Euler-Maclaurin’s formulae. Rend. Circ. Mat. Palermo 54, 259–272 (2005). https://doi.org/10.1007/BF02874640
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DOI: https://doi.org/10.1007/BF02874640