, Volume 34, Issue 2, pp 95-100
Date: 19 Jan 2011

Indefinite summation of rational functions with additional minimization of the summable part

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An algorithm of indefinite summation of rational functions is proposed. For a given function f(x), it constructs a pair of rational functions g(x) and r(x) such that f(x) = g(x + 1) − g(x) + r(x), where the degree of the denominator of r(x) is minimal, and, when this condition is satisfied, the degree of the denominator of g(x) is also minimal.

Original Russian Text © S.P. Polyakov, 2008, published in Programmirovanie, 2008, Vol. 34, No. 2.