Mathematica files with the results for the master integrals.
3 loops 2 loops
exact MI.m MI2l.m
expanded in x MIexp.m MI2lexp.m
In order to use the results for three-loop master integrals, start
Mathematica and say
S=Get[".../MI.m"];
(where ... should be replaced by the path to the file). Then, for example,
the master integral 4.8a with the accuracy up to ep^1 is
M^(-6*ep)*Exp[-3*EulerGamma*ep] times the expression
Sum[MI[p4n8a,i][x]*ep^i,{i,-3,1}]/.S
(for two-loop master integrals from MI2l.m, the prefactor is
M^(-4*ep)*Exp[-2*EulerGamma*ep]). The exact analytical results are
in terms of harmonic polylogarithms (HPL). The files MIexp.m and MI2lexp.m
can be used in the same way, and contain expansions in x.
In the paper
"Matching QCD and HQET heavy-light currents at three loops"
S. Bekavac, A.G. Grozin, P. Marquard, J.H. Piclum, D. Seidel, M. Steinhauser,
arXiv:0911.3356
two more coefficients, MI[p5n2,0][x] and MI[p5n2a,0][x], could be obtained,
which are also included in MI.m.