Positivity of Szegö’s Rational Function
نویسنده
چکیده
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 demonstrate how to apply the transformation to prove a 4-dimensional generalization of the above function, continue with a brief discussion concerning the optimality of this transformation, and close with an elementary proof of a conjecture raised by Kauers.
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