Geodesic
A Note on the Minimality Problem in Indefinite Summation of Rational Functions
Séminaire lotharingien de combinatoire, Tome 31 (1993)

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

Given a rational function f, the problem of indefinite summation is to find rational functions h and r such that f(n) = h(n+1) - h(n) + r(n). We are interested in solutions (h,r) with both h and r of minimal degree in the denominator. Our observations prove that the modification of Abramov's algorithm proposed in ("Algorithmen zur Summation rationaler Funktionen," Diploma Thesis, Univ. Erlangen-Nürnberg, 1992; "Algorithms for indefinite summation of rational functions in Maple," The Maple Techn. Newsletter 2 (1995)) produces such minimal solutions for a certain class of rational summands. The following versions are available: 
@article{SLC_1993_31_a1,
     author = {Roberto Pirastu},
     title = {A {Note} on the {Minimality} {Problem} in {Indefinite} {Summation} of {Rational} {Functions}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {31},
     year = {1993},
     url = {http://geodesic.mathdoc.fr/item/SLC_1993_31_a1/}
}
TY  - JOUR
AU  - Roberto Pirastu
TI  - A Note on the Minimality Problem in Indefinite Summation of Rational Functions
JO  - Séminaire lotharingien de combinatoire
PY  - 1993
VL  - 31
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_1993_31_a1/
ID  - SLC_1993_31_a1
ER  - 
%0 Journal Article
%A Roberto Pirastu
%T A Note on the Minimality Problem in Indefinite Summation of Rational Functions
%J Séminaire lotharingien de combinatoire
%D 1993
%V 31
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_1993_31_a1/
%F SLC_1993_31_a1
Roberto Pirastu. A Note on the Minimality Problem in Indefinite Summation of Rational Functions. Séminaire lotharingien de combinatoire, Tome 31 (1993). http://geodesic.mathdoc.fr/item/SLC_1993_31_a1/