Non-Holonomicity of Sequences Defined via Elementary Functions

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dc.creatorBell, Jason P.
dc.creatorGerhold, Stefan
dc.creatorKlazar, Martin
dc.creatorLuca, Florian
dc.date2006-05-05
dc.date.accessioned2026-07-07T07:13:56Z
dc.date.available2026-07-07T07:13:56Z
dc.descriptionWe present a new method for proving non-holonomicity of sequences, which is based on results about the number of zeros of elementary and of analytic functions. Our approach is applicable to sequences that are defined as the values of an elementary function at positive integral arguments. We generalize several recent results; e.g., non-holonomicity of the logarithmic sequence is extended to rational functions involving $\log n$. Moreover, we show that the sequence that arises from evaluating the Riemann zeta function at odd integers is not holonomic.
dc.identifierhttps://arxiv.org/abs/math/0605142
dc.identifierhttp://arxiv.org/abs/math/0605142
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112670
dc.subjectCombinatorics
dc.subject11B37; 11B83
dc.titleNon-Holonomicity of Sequences Defined via Elementary Functions
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