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 its domain of analyticity. 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.
Harshbarger, Stephanie L. and Willis, Barton L.
The Binomial Transform of P-Recursive Sequences And the Dilogarithm Function,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 15,
2, Article 19.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss2/19