An application of the Euler-MacLaurin summation formula for estimating the order of approximation of sampling-type series

In this paper we establish a quantitative estimate for the order of approximation for the generalized and the Kantorovich sampling series based upon kernels with asymptotic decay as the function u−2, that are characterized by an infinite first order discrete absolute moment. The key point of the above proof is provided by the application of a special case of the Euler-MacLaurin summation formula. Concrete examples are discussed, such as the critical case of the Fejér kernel.