Positivity of Szegö’s rational function

We 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 function 1 (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 demon-strate 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 tha