β Scribed by Yiu-Kwong Man
No coin nor oath required. For personal study only.
A decision procedure for finding closed forms for indefinite summation of polynomials, rational functions, quasipolynomials and quasirational functions is presented. It is also extended to deal with some non-hypergeometric sums with rational inputs, which are not summable by means of Gosper's algorithm. Discussion of its implementation, analysis of degree bounds and some illustrative examples are included.
π SIMILAR VOLUMES
The problem of computing a closed form for sums of special functions arises in many parts of mathematical and computer science, especially in combinatorics and complexity analysis. Here we discuss two algorithms for indefinite summation of rational functions, due to Abramov (1975) and Paule (1993).