Séminaire Lotharingien de Combinatoire, B05e (1981), 11 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1982, 182/S-04, p.
84-94.]
Joe Gillis, Bruce Reznick and Doron Zeilberger
On Elementary Methods in Positivity Theory
Abstract.
We raise conjectures concerning the positivity of the power series
coefficients of multi-variate rational functions. We also give
a short proof of a result of Askey and Gasper that
(1-x-y-z+4xyz)-b has positive power series
coefficients for b>=(\sqrt{17}-3)/2. We show how
Ismail and Tanharkar's proof that
(1-(1-L)x-Ly-Lxz-(1-L)yz+xyz)-a
(where 0<=L<=1)
has positive power series coefficients for a=1 implies
Koornwinder's result that it does so for a>=1.
The following version is available:
The paper has been finally published under the same title in
SIAM J. Math. Anal. 14 (1983), 396-398.