A summation formula for the finite sum of form such as Σƒ(i)ti

Abstract

In this paper, we discussed a kind of summation formula for the finite sum of form such as Σƒ(i)ti, which is based on two representations of a (n + 1) -th continuous differentiable function ƒ(z) by the Bernoulli function or the Eulerian function. For ƒ(z) be a polynomial in z of degree n, we educed an especial summation formula, which has wide applications in numerical calculation.