We consider summation of consecutive values Φ(v), Φ(v + 1), ..., Φ(w) of a meromorphic function Φ(z) where v, w ∈ ZZ. 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 ord L = 1). The notion of bottom summation which covers the case where Φ(z) has poles in ZZ is introduced.
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