  Relations have been derived which establish connection between a scalar or a
vector functions and the integral of Laplace operator of these functions (the
integral property of Laplace operator). The integral property of Laplace
operator was employed to obtain relations expressing the electric field in
terms of the charge gradient. It is demonstrated that these relations define
the same field which is described by the well known classical expressions for
the electric field. It is shown that these proposed expressions represent
actually a particular case of the general theory of generalized functions. This
approach is illustrated by calculation of an electric field performed with the
proposed formalism.
