The extended Routh´s table in the complex case

The construction of the Routh´s table in the complex case is extended to the special case of vanishing leading array elements without introducing the classical ε method. It is shown that it is always possible to associate to any polynomial G with complex or real coefficients an extended Routh´s table and that the number of sign changes in the first column of this table equals the number of zeros of G with positive real part