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.
Type de document :
Pré-publication, Document de travail
24 pages. 2009
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Contributeur : Bruno Salvy <>
Soumis le : vendredi 12 juin 2009 - 21:04:25
Dernière modification le : vendredi 25 mai 2018 - 12:02:05

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



Philippe Flajolet, Stefan Gerhold, Bruno Salvy. Lindelöf Representations and (Non-)Holonomic Sequences. 24 pages. 2009. 〈inria-00394936〉



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