We treat the univariate interpolation problem {f (xj) = yj }jjLi for polynomial and rational functions. Developing the approach by C.Jacobi, we represent the interpolants by virtue of the Hankel polynomials generated by the sequences {jji. xyj/W'(xj)}fc£N and {jji. xj/(yjW'(xj))}fceN; here W(x) = J=i(x - xj). The obtained results are applied for the error correction problem, i.e. the problem of reconstructing the polynomial from a redundant set of its values some of which are probably erroneous. The problem of evaluation of the resultant of polynomials p(x) and q(x) from the set of their values is also tackled within the framework of this approach.