  The aim of this work is the derivation of two approximated expressions for
the two dimensional Gaussian Q-function, $Q(x,y;\rho)$. These expressions are
highly accurate and are expressed in closed-form. Furthermore, their algebraic
representation is relatively simple and therefore, convenient to handle both
analytically and numerically. This feature is particularly useful for two
reasons: firstly because it renders the derived expressions useful mathematical
tools that can be utilized in numerous analytic performance evaluation studies
in digital communications under fading; secondly because the two dimensional
Gaussian Q-function is neither tabulated nor a built-in function in popular
mathematical software packages such as $Maple$, $Mathematica$ and $Matlab$.
