On the bottom summation
- First Online:
- Cite this article as:
- Abramov, S.A. & Petkovšek, M. Program Comput Soft (2008) 34: 187. doi:10.1134/S0361768808040014
- 20 Views
We consider summation of consecutive values (φ(v), φ(v + 1), ..., φ(w) of a meromorphic function φ(z), where v, w ∈ ℤ. We assume that φ(z) satisfies a linear difference equation L(y) = 0 with polynomial coefficients, and that a summing operator for L exists (such an operator can be found—if it exists—by the Accurate Summation algorithm, or, alternatively, by Gosper’s algorithm when ordL = 1). The notion of bottom summation which covers the case where φ(z) has poles in ℤ is introduced.