On the evaluation of sums of exponentiated multiples of generalized Catalan number linear combinations using a hypergeometric approach
AuthorsLarcombe, Peter J.
AffiliationUniversity of Derby
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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.
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. 259-270
PublisherThe Fibonacci Association
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