Positivity of Szegö's rational function

AbstractWe consider the problem of deciding whether a given rational function has a power series expansion with all its coefficients positive. Introducing an elementary transformation that preserves such positivity we are able to provide an elementary proof for the positivity of Szegö's function1(1−x)(1−y)+(1−y)(1−z)+(1−z)(1−x) which has been at the historical root of this subject starting with Szegö. We then demonstrate how to apply the transformation to prove a 4-dimensional generalization of the above function, and close with discussing the set of parameters (a,b) such that11−(x+y+z)+a(xy+yz+zx)+bxyz has positive coefficients