Minimal decomposition of indefinite hypergeometric sums
Sergei A. Abramov, Marko Petkovšek · 2001
We present an algorithm which, given a hypergeometric term T(n), constructs hypergeometric terms T1(n) and T2(n) such that T(n) = T1(n + 1) -T1(n) + T2(n), and T2(n) is minimal in some sense. This solves the decomposition problem for indefinite sums of hypergeometric terms: T1(n + 1) - T1(n) is the “summable part” and T2(n) the “non-summable part” of T(n).