Geodesic
A Note on the Minimality Problem in Indefinite Summation of Rational Functions
Séminaire lotharingien de combinatoire, Tome 31 (1993) Cet article a éte moissonné depuis la source Séminaire Lotharingien de Combinatoire website

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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},
     year = {1993},
     volume = {31},
     url = {http://geodesic.mathdoc.fr/item/SLC_1993_31_a1/}
}
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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/