Abstract
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.
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Abramov, S.A., Petkovšek, M. On the bottom summation. Program Comput Soft 34, 187–190 (2008). https://doi.org/10.1134/S0361768808040014
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DOI: https://doi.org/10.1134/S0361768808040014