Abstract
In this Letter we continue the calculation of master integrals for massless three-loop form factors by giving analytical results for those integrals which are relevant for the fermionic contributions proportional to NF2, NF⋅N, and NF/N. Working in dimensional regularisation, we express one of the integrals in a closed form which is exact to all orders in ϵ, containing Γ-functions and hypergeometric functions of unit argument. In all other cases we derive multiple Mellin–Barnes representations from which the coefficients of the Laurent expansion in ϵ are extracted in an analytical form. To obtain the finite part of the three-loop quark and gluon form factors, all coefficients through transcendentality six in the Riemann ζ-function have to be included.
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