Geodesic
On Elementary Methods in Positivity Theory
Séminaire lotharingien de combinatoire, Tome 05 (1981)

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. 

@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},
     publisher = {mathdoc},
     volume = {05},
     year = {1981},
     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
PB  - mathdoc
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
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_1981_05_a4/
%F SLC_1981_05_a4
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/