Indefinite summation of rational functions with additional minimization of the summable part
S. P. Polyakov · Programming and Computer Software · 2008
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.