  We estimate the asymptotics of spherical integrals when the rank of one
matrix is finite. We show that it is given in terms of the R-transform of the
spectral measure of the full rank matrix and give a new proof of the fact that
the R-transform is additive under free convolution. These asymptotics also
extend to the case where one matrix has rank one but complex eigenvalue, a
result related with the analyticity of the corresponding spherical integrals.
