AN ARGUMENT PRINCIPLE FOR REAL FUNCTIONS AND NONHARMONIC SINGULARITIES IN THE PLANE

A real, rational function r(t) determines an argument function 𝜗(t), whose increment Δ𝜗(t) relates the numbers of distinct, real zeros and poles of r(t). The present expository note derives such a result, and explains its relevance to the index for a certain class of planar singularities.