Positivity of Szegö's rational function (Q931842)

A rational function is called positive if all its Taylor coefficients are positive. The author considers the problem of deciding whether a given rational function is positive. Using an operator that preserves positivity and symmetry, a proof for the positivity of Szegö function \[ \frac{1}{(1-x)(1-y)+(1-y)(1-z)+(1-z)(1-x)} \] is provided. Then the author demonstrates how to apply the transformation to prove a 4-dimensional generalization of the Szegö function. Finally, the paper is completed by discussing the set of parameters \((a,b)\) such that \[ \frac{1}{1-(x+y+z)+a(xy+yz+zx)+bxyz} \] has positive coefficients.