  The paper discusses some properties of the modulus $|W_{k,m}(z)|$ of the
Whittaker function $W_{k,m}(z)$. In particular, completely monotone functions
expressed in terms of $|W_{k,m}(z)|$ are found. The results follow from an
integral representation for products of Whittaker functions due to Erd\'elyi
(1938).
