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I am referring to the following version of the theorem, in the setting of the Lebesgue integral. Theorem Let $f: [a,b] \rightarrow \bf R$ be an everywhere differentiable function whose derivative is ...

Introduction The Euler–Maclaurin summation formula is as follows for a positive integer $p$ and a continuous function $f(\cdot)$ that is $p$ times continuously differentiable on the interval $[m,n]$ : ...