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

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.

6 pages, 2 figures

References in corpus (2)

• Generalized binomial transform applied to the divergent series
• Generating Function Transformations Related to Polylogarithm Functions and the $k$-Order Harmonic Numbers