Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4625040 | Advances in Applied Mathematics | 2008 | 10 Pages |
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 function1(1âx)(1ây)+(1ây)(1âz)+(1âz)(1âx) 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 that11â(x+y+z)+a(xy+yz+zx)+bxyz has positive coefficients.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Armin Straub,