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dc.contributor.authorLarcombe, Peter J.
dc.date.accessioned2016-11-16T16:05:05Z
dc.date.available2016-11-16T16:05:05Z
dc.date.issued2016-08
dc.identifier.citationLarcombe, P. J. (2016) 'On the evaluation of sums of exponentiated multiples of generalized Catalan number linear combinations using a hypergeometric approach', Fibonacci Quarterly, 54 (3), pp. 259-270en
dc.identifier.issn0015-0517
dc.identifier.urihttp://hdl.handle.net/10545/620868
dc.description.abstractInfinite series comprising exponentiated multiples of p-term linear combinations of Catalan numbers arise naturally from a related power series expansion for sin(2pα) (in odd powers of sin(α)) which itself has an interesting history. In this article some explicit results generated previously by the author (for p = 1, 2, 3) are discussed in the context of this general problem of series summation, and new evaluations made for the cases p = 4, 5 by way of further examples. A powerful hypergeometric approach is adopted which offers, from the analytical formulation developed, a means to achieve these particular evaluations and in principle many others for even greater values of p.
dc.language.isoenen
dc.publisherThe Fibonacci Associationen
dc.relation.urlhttp://www.fq.math.ca/54-3.htmlen
dc.relation.urlhttp://www.fq.math.ca/index.htmlen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.subjectDiscrete mathematicsen
dc.subjectApplied mathematicsen
dc.titleOn the evaluation of sums of exponentiated multiples of generalized Catalan number linear combinations using a hypergeometric approachen
dc.typeArticleen
dc.contributor.departmentUniversity of Derbyen
dc.identifier.journalFibonacci Quarterlyen
refterms.dateFOA2019-10-14T13:59:20Z
html.description.abstractInfinite series comprising exponentiated multiples of p-term linear combinations of Catalan numbers arise naturally from a related power series expansion for sin(2pα) (in odd powers of sin(α)) which itself has an interesting history. In this article some explicit results generated previously by the author (for p = 1, 2, 3) are discussed in the context of this general problem of series summation, and new evaluations made for the cases p = 4, 5 by way of further examples. A powerful hypergeometric approach is adopted which offers, from the analytical formulation developed, a means to achieve these particular evaluations and in principle many others for even greater values of p.


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