On the Euler-Maclaurin formula
The classical Euler-Maclaurin formula \[ \sum^M_{k=N} \varphi (k)= \int^M_N \varphi (x)+ {\varphi(N) +\varphi(M) \over 2} +\sum^q_{j=2} c_j\bigl[ \varphi^{(j-1)} (M)-\varphi^{(j-1)} (N)\bigr] +Rq, \] relating the integral of a function \(\varphi\in C^q(N,M)\) to the relevant finite sum, is generalized to distributions. The case of a power behaviour of \(\varphi\) at the ends of the interval and the case when \(\varphi\) has discontinuities inside the interval are studied.
scientific article; zbMATH DE number 1061848