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Lindelöf Representations and (Non-)Holonomic Sequences

Abstract : Various sequences that possess explicit analytic expressions can be analysed asymptotically through integral representations due to Lindelöf, which belong to an attractive but largely forgotten chapter of complex analysis. One of the outcomes of such analyses concerns the non-existence of linear recurrences with polynomial coefficients annihilating these sequences, and, accordingly, the non-existence of linear differential equations with polynomial coefficients annihilating their generating functions. In particular, the corresponding generating functions are transcendental. Asymptotics of certain finite difference sequences come out as a byproduct of our approach.
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Preprints, Working Papers, ...
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https://hal.inria.fr/inria-00394936
Contributor : Bruno Salvy <>
Submitted on : Friday, June 12, 2009 - 9:04:25 PM
Last modification on : Tuesday, August 6, 2019 - 1:10:12 AM

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  • HAL Id : inria-00394936, version 1
  • ARXIV : 0906.1957

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Philippe Flajolet, Stefan Gerhold, Bruno Salvy. Lindelöf Representations and (Non-)Holonomic Sequences. 2009. ⟨inria-00394936⟩

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