Properties (in particular functional relations and special values) of the functions \[ (-1)^{n+p-1}(n-1)! p! S_{n,p}(z)=\int^{1}_{0}\log^{n-1}t \log^ p(1-zt)(dt/t), \] \[ (-1)^{n+p-1}(n-1)! p! L_{n,p}(z)=\int^{z}_{0}\log^{n-1}t \log^ p(1-t)(dt/t), \] \[ (-1)^{n-1}(n-1)! p! M_{n,p}(z)=\int^{z}_{0}\log^{n-1}t \log^ p(1+t)(dt/t), \] which play a role in the computation of higher order radiative corrections in quantum electrodynamics, are discussed for complex z and positive integers n and p. The first function is a generalization of the well- known polylogarithms \((p=1)\). The discussion is based on results published by Nielsen early this century in a little-known monograph.