On the non-holonomic character of logarithms, powers, and the n-th prime function

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dc.creatorFlajolet, Philippe
dc.creatorGerhold, Stefan
dc.creatorSalvy, Bruno
dc.date2005-01-22
dc.date.accessioned2026-07-07T09:23:37Z
dc.date.available2026-07-07T09:23:37Z
dc.descriptionWe establish that the sequences formed by logarithms and by "fractional" powers of integers, as well as the sequence of prime numbers, are non-holonomic, thereby answering three open problems of Gerhold [Electronic Journal of Combinatorics 11 (2004), R87]. Our proofs depend on basic complex analysis, namely a conjunction of the Structure Theorem for singularities of solutions to linear differential equations and of an Abelian theorem. A brief discussion is offered regarding the scope of singularity-based methods and several naturally occurring sequences are proved to be non-holonomic.
dc.description13 pages
dc.identifierhttps://arxiv.org/abs/math/0501379
dc.identifierhttp://arxiv.org/abs/math/0501379
dc.identifierThe Electronic Journal of Combinatorics, vol. 11, no. 2, article A2. 2005.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155798
dc.subjectCombinatorics
dc.subject05A19; 33E30
dc.titleOn the non-holonomic character of logarithms, powers, and the n-th prime function
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