  Resultants are important special functions used in description of non-linear
phenomena. Resultant $R_{r_1, ..., r_n}$ defines a condition of solvability for
a system of $n$ homogeneous polynomials of degrees $r_1, ..., r_n$ in $n$
variables, just in the same way as determinant does for a system of linear
equations. Unfortunately, there is a lack of convenient formulas for resultants
when the number of variables is large. In this paper we use Cauchy contour
integrals to obtain a polynomial formula for resultants, which is expected to
be useful in applications.
