"I try to type that kind of function myself using MeijerG, but it doesn't work. "
That is supposed to be the MeijerG used by Mathematica. If you find a difference in output between that formula and the output of MeijerG, please send a notebook file documenting the discrepancy to email@example.com. (The output of $Version would be helpful, too.)
See also http://reference.wolfram.com/mathematica/ref/MeijerG.html,
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