Abstract
Consider the problem of obtaining asymptotic information about a multidimensional arrayof numbers ar, given the generating function\( F\left( z \right) = \sum\nolimits_{r} {{{a}_{r}}} {{z}^{r}} \) When F is meromorphic, it is known how to obtain various asymptotic series for a r in decreasing powers of \( \left| r \right|\).The purpose of this note is to show thatwhen the pole set of F has singularities of a certain kindthen there can be only finitely many terms in such an asymptotic series. As a consequence, in the presence of a singularity of this kind, the whole asymptotic series for ar, is an effectively computable object.
Research supported in part by National Science Foundation grant # DMS 9803249
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Pemantle, R. (2000). Generating functions with high-order poles are nearly polynomial. In: Gardy, D., Mokkadem, A. (eds) Mathematics and Computer Science. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8405-1_26
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DOI: https://doi.org/10.1007/978-3-0348-8405-1_26
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