Indefinite summation of rational functions with additional minimization of the summable part
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- Polyakov, S.P. Program Comput Soft (2008) 34: 95. doi:10.1134/S0361768808020060
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.