  Friedberg, Hoffstein and Lieman have constructed two related multiple
Dirichlet series from quadratic and higher-order $L$-functions and Gauss sums.
We compute these multiple Dirichlet series explicitly in the case of the
rational function field. This is done by utilizing the functional equation of
the $L$-functions and the functional equation relating the two multiple
Dirichlet series. We also point out a very simple correspondence between these
series and their $p$-parts.
