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Given the polynomial in s which describes the reciprocal of the transfer function of the circuit to be synthesized, the recurrent determinant may be determined. The continuant determinant is evaluated by a logical sequence of operations on the recurrent determinant. The values of the elements of the continuant determine either the gains of the amplifiers in the circuit when the component values are specified or the component values when the amplifier gains are specified. The reverse procedure of producing the recurrent from the continuant is also described and from the recurrent the reciprocal of the transfer function of the network may be obtained.