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arXiv · 1207.3824

Generalised ladders and single-valued polylogarithms

J. M. Drummond
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Abstract

We introduce and solve an infinite class of loop integrals which generalises the well-known ladder series. The integrals are described in terms of single-valued polylogarithmic functions which satisfy certain differential equations. The combination of the differential equations and single-valued behaviour allow us to explicitly construct the polylogarithms recursively. For this class of integrals the symbol may be read off from the integrand in a particularly simple way. We give an explicit formula for the simplest generalisation of the ladder series. We also relate the generalised ladder integrals to a class of vacuum diagrams which includes both the wheels and the zigzags.

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J. M. Drummond. 2012-07-16. Generalised ladders and single-valued polylogarithms. https://doi.org/10.1007/jhep02(2013)092

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