PoS - Proceedings of Science
Volume 383 - MathemAmplitudes 2019: Intersection Theory & Feynman Integrals (MA2019) - Session 2: Intersection Theory, Integral Relations and Applications to Physics
Four-loop master integrals and hypergeometric functions
S. Laporta
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Published on: February 15, 2022
We recall the analytical result of the 4-loop QED contribution
to the electron $g$-$2$ and slope, which contain elliptic constants. We describe the relations between four elliptic constants which have ${}_4F_3$ hypergeometric expressions. In particular we consider a quadratic relation found by Broahurst and Mellit, and, by introducing a free parameter, we generalize it to a new quadratic relation between values of the hypergeometric ${}_4F_3$.
DOI: https://doi.org/10.22323/1.383.0023
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