  The specific heat-phonon spectrum inversion has played a significant role in
solid physics. But for this inherently ill-posed problem, most of the known
solutions are complex both in form and content, although they are rigorous and
perfect. Here we suggest another simpler series solution to this problem, which
can be easily calculated if the ratio of specific heat to temperature can be
expanded into a power series, or specific heat can be expanded asymptotically
and conditionally. Furthermore, we suggest similar solutions to the black-body
radiation inversion.
