Séminaire Lotharingien de Combinatoire, B31b (1993), 7pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1994/021, p. 95-101.]

Roberto Pirastu

A Note on the Minimality Problem in Indefinite Summation of Rational Functions

Abstract. 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.

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