Extended table for eliminating the singularities in Routh´s array

A simple procedure for eliminating the classical ε-method introduced by the Routh-Hurwitz test is given. The procedure extends the construction of the Routh table in the special case of vanishing leading array elements without introducing complementary multiplications. It is shown that it is always possible to associate with any polynomial g an extended Routh table. The number of sign changes in the first column of the table equals the number of zeros of g with positive real part