On the mathematica Mathworld website, it's easy to find the expression for the Meijer G function. However, it is less easy to see if it has some simpler form in terms of other known functions. The specific case I would like to simplify is
MeijerG[{{}, {3 + a, -b}, {{0, 1}, {}}, x^2]
with $a\geq b\geq 0$ and $b\in\mathbb{Z}$ and $x\in(0,1)$. If it helps, I have reason to believe it's related to the hypergeometric function $x^2 {_2 F_1}(-(1 + a);2 + b;2; x^2)$, as they both solve the same differential equation.