Parameterized Telescoping Proves Algebraic Independence of Sums

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dc.creatorSchneider, Carsten
dc.date2008-08-19
dc.date.accessioned2026-07-07T09:59:36Z
dc.date.available2026-07-07T09:59:36Z
dc.descriptionUsually creative telescoping is used to derive recurrences for sums. In this article we show that the non-existence of a creative telescoping solution, and more generally, of a parameterized telescoping solution, proves algebraic independence of certain types of sums. Combining this fact with summation-theory shows transcendence of whole classes of sums. Moreover, this result throws new light on the question why, e.g., Zeilberger's algorithm fails to find a recurrence with minimal order.
dc.descriptionTo appear in Annals of Combinatorics
dc.identifierhttps://arxiv.org/abs/0808.2596
dc.identifierhttp://arxiv.org/abs/0808.2596
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168077
dc.subjectSymbolic Computation
dc.subjectCombinatorics
dc.subjectNumber Theory
dc.titleParameterized Telescoping Proves Algebraic Independence of Sums
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