English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We introduce a class of iterated integrals, defined through a set of linearlyindependent integration kernels on elliptic curves. As a direct generalisationof multiple polylogarithms, we construct our set of integration kernelsensuring that they have at most simple poles, implying that the iteratedintegrals have at most logarithmic singularities. We study the properties ofour iterated integrals and their relationship to the multiple ellipticpolylogarithms from the mathematics literature. On the one hand, we find thatour iterated integrals span essentially the same space of functions as themultiple elliptic polylogarithms. On the other, our formulation allows for amore direct use to solve a large variety of problems in high-energy physics. Wedemonstrate the use of our functions in the evaluation of the Laurent expansionof some hypergeometric functions for values of the indices close to halfintegers.

Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism