Four-loop master integrals and hypergeometric functions Article Swipe
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S. Laporta
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YOU?
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· 2022
· Open Access
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· DOI: https://doi.org/10.22323/1.383.0023
· OA: W4212996312
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.22323/1.383.0023
· OA: W4212996312
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 ${}_4F_3$.
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