TL;DR
This paper reviews the relationship between Feynman integrals and multiple polylogarithms, covering mathematical tools like Mellin-Barnes transformation and shuffle algebras, and explaining how certain integrals evaluate to these functions.
Contribution
It provides a comprehensive overview of the mathematical structures connecting Feynman integrals to multiple polylogarithms, including new insights into their evaluation methods.
Findings
Feynman integrals can be expressed in terms of multiple polylogarithms
Mellin-Barnes transformation aids in evaluating complex integrals
Shuffle algebras help understand the algebraic structure of polylogarithms
Abstract
In this talk I review the connections between Feynman integrals and multiple polylogarithms. After an introductory section on loop integrals I discuss the Mellin-Barnes transformation and shuffle algebras. In a subsequent section multiple polylogarithms are introduced. Finally, I discuss how certain Feynman integrals evaluate to multiple polylogarithms.
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