Four-loop master integrals and hypergeometric functions

Abstract

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 4F3 hypergeometric expressions. In particular we consider a quadratic relation found by Broadhurst and Mellit, and, by introducing a free parameter, we generalize it to a new quadratic relation between values of the hypergeometric 4F3.