Geodesic
On Elementary Methods in Positivity Theory
Séminaire lotharingien de combinatoire, Tome 05 (1981) 
Joe Gillis; Bruce Reznick; Doron Zeilberger. On Elementary Methods in Positivity Theory. Séminaire lotharingien de combinatoire, Tome 05 (1981). http://geodesic.mathdoc.fr/item/SLC_1981_05_a4/
@article{SLC_1981_05_a4,
     author = {Joe Gillis and Bruce Reznick and Doron Zeilberger},
     title = {On {Elementary} {Methods} in {Positivity} {Theory}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {1981},
     volume = {05},
     url = {http://geodesic.mathdoc.fr/item/SLC_1981_05_a4/}
}
TY  - JOUR
AU  - Joe Gillis
AU  - Bruce Reznick
AU  - Doron Zeilberger
TI  - On Elementary Methods in Positivity Theory
JO  - Séminaire lotharingien de combinatoire
PY  - 1981
VL  - 05
UR  - http://geodesic.mathdoc.fr/item/SLC_1981_05_a4/
ID  - SLC_1981_05_a4
ER  - 
%0 Journal Article
%A Joe Gillis
%A Bruce Reznick
%A Doron Zeilberger
%T On Elementary Methods in Positivity Theory
%J Séminaire lotharingien de combinatoire
%D 1981
%V 05
%U http://geodesic.mathdoc.fr/item/SLC_1981_05_a4/
%F SLC_1981_05_a4

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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 paper has been finally published under the same title in SIAM J. Math. Anal. 14 (1983), 396-398.