Analytic Solutions of Linear Difference Equations, Formal Series, and Bottom Summation
نویسندگان
چکیده
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 ordL = 1). The notion of bottom summation which covers the case where φ(z) has poles in ZZ is introduced.
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