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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