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      The binomial transform of p-recursive sequences and the dilogarithm function

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          Abstract

          Using a generalized binomial transform and a novel binomial coefficient identity, we will show that the set of p-recursive sequences is closed under the binomial transform. Using these results, we will derive a new series representation for the dilogarithm function that converges on \(\mathbf{C} \, \backslash \, [1,\infty)\). Finally, we will show that this series representation results in a scheme for numerical evaluation of the dilogarithm function that is accurate, efficient, and stable.

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          A holonomic systems approach to special functions identities

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            Pracniques: further remarks on reducing truncation errors

             W. Kahan (1965)
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              Analytic continuation of the3F2hypergeometric series

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                Author and article information

                Journal
                15 October 2019
                Article
                1910.06928

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                33E20
                6 pages, 2 figures
                math.CA

                Mathematics

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