Hypergeometric Functions and Feynman Diagrams

DOI10.1007/978-3-030-80219-6_9zbMATH Open1489.33010arXiv2012.14492OpenAlexW4211100443MaRDI QIDQ5022177

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Publication date: 18 January 2022

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Abstract: The relationship between Feynman diagrams and hypergeometric functions is discussed. Special attention is devoted to existing techniques for the construction of the $epsilon$-expansion. As an example, we present a detailed discussion of the construction of the epsilon-expansion of the Appell function $F_3$ around rational values of parameters via an iterative solution of differential equations. As a by-product, we have found that the one-loop massless pentagon diagram in dimension $d=3-2epsilon$ is not expressible in terms of multiple polylogarithms. Another interesting example is the Puiseux-type solution involving a differential operator generated by a hypergeometric function of three variables. The holonomic properties of the $F_N$ hypergeometric functions are briefly discussed.

Full work available at URL: https://arxiv.org/abs/2012.14492

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