Positivity of Szegö's rational function

Abstract: 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 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 such that has positive coefficients. [Copyright &y& Elsevier]