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 epsilon 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.<
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