  This work is devoted to the derivation of novel analytic results for special
functions which are particularly useful in wireless communication theory.
Capitalizing on recently reported series representations for the Nuttall
$Q{-}$function and the incomplete Toronto function, we derive closed-form upper
bounds for the corresponding truncation error of these series as well as
closed-form upper bounds that under certain cases become accurate
approximations. The derived expressions are tight and their algebraic
representation is rather convenient to handle analytically and numerically.
Given that the Nuttall${-}Q$ and incomplete Toronto functions are not built-in
in popular mathematical software packages, the proposed results are
particularly useful in computing these functions when employed in applications
relating to natural sciences and engineering, such as wireless communication
over fading channels.
