Remark 15.17. If x ∈ N0, x ≤ n, the second term vanishes, so the right side becomes just
independent of x. The case x = n is found in [Kaucky´ 75, (6.7.2)].
A similar but more specialized formula is the following:
Theorem 15.18. For all p ∈ N, n∑
) [−p]k[p]n−kHp+k−1 = (−1)n(n− 1)!. (15.12)
Proof: We write the sum as
[p]nHp−1 + n∑