Programming and Computer Software

, Volume 34, Issue 2, pp 95-100

First online:

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

  • S. P. PolyakovAffiliated withComputing Center, Russian Academy of Sciences Email author 

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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.