Rational Reductions for Holonomic Sequences

Given a holonomic sequence F(n), the author characterizes rational functions r(n) so that r(n)F(n) can be summable. The author provides upper and lower bounds on the degree of the numerator of r(n) and shows the denominator of r(n) can be read from annihilators of F(n). This illustration provides the so-called rational reductions which can be used to generate new multi-sum equalities and congruences from known ones.