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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.

### Most cited references4

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### A holonomic systems approach to special functions identities

(1990)
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### Pracniques: further remarks on reducing truncation errors

(1965)
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### Analytic continuation of the3F2hypergeometric series

(2016)
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### Author and article information

###### Journal
15 October 2019
###### Article
1910.06928

33E20
6 pages, 2 figures
math.CA

Mathematics