Mathematical properties of the vacuum polarization function

This paper is an investigation of certain mathematical properties of the vacuum polarization function (s). We show that (s) is a Herglotz function, has no complex zeroes, and belongs to the class of functions called typically real. In addition, we obtain upper bounds on the higher derivatives of (s), at s=0, given that we know the value of the first derivative at that point.Research supported in part by NASA Grant NSG-8035