Master integrals for fermionic contributions to massless three-loop form factors

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 N2F, N-F.N, and N-F/N. Working in dimensional regularisation, we express one of the integrals in a closed form which is exact to all orders in c, containing Gamma-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 E 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-function have to be included. (C) 2008 Elsevier B.V. All rights reserved.