I have an instance of the Meijer G function (using the definition from http://en.wikipedia.org/wiki/Meijer_G-Function, first equation there) that seems like, given its simplicity, it should be expressible in terms of another special function. The instance is: $G\left(z\Bigg|\begin{matrix}- & - \\ 0,\tfrac{1}{2},1 & -\end{matrix}\right)=\frac{1}{2\pi i}\int_{\gamma_L}ds\, z^{-s} \frac{1}{\Gamma(-s)\Gamma(\tfrac{1}{2}-s)\Gamma(1-s)}$.
Thanks in advance for your scholarly input. >wink<
You can write this function as an abramowitz function, it may or may not be easier to deal with.
MeijerG[{{}, {}}, {{0, 1/2, 1}, {}}, x^2/4]/(2 Sqrt[pi]) = Int_0^inf c^1 Exp (-c^2-x/c) dc
Source: Evaluate this integral in Mathematica and you should get the corresponding Meijer G function.