On some bivariate Hermite type interpolation and numerical integration formulae

In this paper we present a bivariate interpolation formula using four multiple nodes and then the corresponding numerical integration formula for a double integral extended over a rectangular domain. The cubature formula (3.1) represents an extension to two variables of the Hermite quadrature formula (1.1). At (4.1) we give an integral representation for the remainder of this cubature formula.