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

Abstract

A real, rational function $r(t)$ determines an argument function $𝜗(t)$, whose increment $\mathrm{\Delta }𝜗(t)$ 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.