Abstract
The error of the Markoff's formula, which is a differentiation of the Newton forward- or backward-difference formula, is analysed. We firs derived the integral remainder for the Newton interpolation formula. This follows the Markoff's formula with integral remainder. The kernel functions (Peano kernels) of the integral remainder for the Markoff's formula, which are represented in terms of the truncated power functions, can be rewritten in terms of the normalized B-splines. We also derived the integeral remainders of modified and generalized Markoff's formulas. This principle can be applied to the Gregory's formula.
