  Linear non-compact operators are difficult to study because they do not exist
in the finite dimensional world. Recently, Math\'{e} and Hofmann studied the
singular values of the compact composition of the non-compact Hausdorff moment
operator and the compact integral operator and found credible arguments, but no
strict proof, that those singular values fall only slightly faster than those
of the integral operator alone. However, the fact that numerically the singular
values of the combined operator fall exponentially fast was not mentioned. In
this note, we provide the missing numerical results and provide an explanation
why the two seemingly contradicting results may both be true.
