Derivation of the errors involved in Hermite interpolation and their applications to quadrature formulae

Divided differences are presented to derive closed-form for the error involved in Hermite interpolation formulae for the class of functions, which need not be sufficiently differentiable. As applications of these formulae the error estimates in the known Gaussian quadrature formulae for regular and singular integrals are taken up. Some examples are considered for numerical experiments.