Euler-Maclaurin Integration Formulas

Author

Eric W. Weisstein
June 5, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/NumericalMath/Euler-MaclaurinIntegrationFormulas.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Euler-MaclaurinIntegrationFormulas.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Formula

Integrate[f[k],{k,0,n}]-(f[0]+f[n])/2+Sum[BernoulliB[2k]/(2k)! (Derivative[2k-1][f][n]-Derivative[2k-1][f][0]),{k,4}]//TraditionalForm