Extended interpretation of a Steiglitz--Zemanian lemma on positive real functions

The easy recognisibility of positive reality, contained in a lemma due to Steiglitz and Zemanian for the case of rational functions consisting of a multiple real pole and multiple real zero, will be extended so as to include possible multiple complex poles and zeros. The emphasis will therefore be on multiplicity and complexity, such as may be exhibited by the poles and zeros of immittance functions.