A discrete analogue of Euler's summation formula (Q1810151)

The classical version of the Euler-MacLaurin sum formula relates a definite integral of a given function to the mean value of its function values on an equispaced grid by showing that the difference of these two quantities can be expressed with the help of Bernoulli polynomials and derivatives of the function under consideration. In the paper under review, a discretized version of this formula is derived where the integral is replaced by a mean value of function values on a finer but still equispaced grid, and the derivatives are replaced by finite differences.