Abstract
Ability to evaluate contour integrals is central to both the theory and the utilization of analytic functions. We present here a complex plane realization of the Euler–Maclaurin formula that includes weights also at some grid points adjacent to each end of a line segment (made up of equispaced grid points, along which we use the trapezoidal rule). For example, with a $5\times 5$ ‘correction stencil’ (with weights about two orders of magnitude smaller than those of the trapezoidal rule), the accuracy is increased from $2$nd to $26$th order.