# Special values of multiple polylogarithms

@article{Borwein1999SpecialVO, title={Special values of multiple polylogarithms}, author={Jonathan Michael Borwein and David M. Bradley and David John Broadhurst and Petr Lisonek}, journal={Transactions of the American Mathematical Society}, year={1999}, volume={353}, pages={907-941} }

Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and high-energy physics. More recently, we have been forced to consider multidimensional extensions encompassing the classical polylogarithm, Euler sums, and the Riemann zeta function. Here, we provide a general framework within which…

## 317 Citations

Duality Formulas of the Special Values of Multiple Polylogarithms

- Mathematics
- 2003

The special values of multiple polylogarithms, which include multiple zeta values, appear in several fields of mathematics and physics. Many kinds of their linear relations have been investigated, as…

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- 2015

In this paper, we define a finite sum analogue of multiple polylogarithms inspired by the work of Kaneko and Zagier (in the article “Finite multiple zeta values” in preparation) and prove that they…

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In this paper we consider iterated integrals of multiple polylogarithm functions and prove some explicit relations of multiple polylogarithm functions. Then we apply the relations obtained to find…

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- 2012

We describe a general computational scheme for evaluation of a wide class of number-theoretical functions. We avoid asymptotic expansions in favor of manifestly convergent series that lend themselves…

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- MathematicsAsian-European Journal of Mathematics
- 2019

The connection between polylogarithmic functions and Euler sums is well-known. In this paper, we explore the representation and many connections between integrals of products of polylogarithmic…

Integrals of polylogarithmic functions with negative argument

- Mathematics, PhilosophyActa Universitatis Sapientiae, Mathematica
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Abstract The connection between polylogarithmic functions and Euler sums is well known. In this paper we explore the representation and many connections between integrals of products of…

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