Closed form evaluations of some series comprising sums of exponentiated multiples of two-term and three-term Catalan number linear combinations
Authors
Larcombe, Peter J.Affiliation
University of DerbyIssue Date
2015-08
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Closed form evaluations of some infinite series comprising sums of exponentiated multiples of two-term and three-term Catalan number linear combinations are presented using three contrasting approaches. Known power series expansions of the trigonometric functions sin(4α) and sin(6α) each readily give a set of (four) results which are reformulated via a hypergeometric route and, additionally, using only the generating function for the Catalan sequence; the latter two methods are shown to be connected.Citation
Larcombe, P. J. (2015) 'Closed form evaluations of some series comprising sums of exponentiated multiples of two-term and three-term Catalan number linear combinations', Fibonacci Quarterly, 53 (3)Publisher
The Fibonacci AssociationJournal
Fibonacci QuarterlyType
ArticleLanguage
enISSN
0015-0517Collections
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