Please, can the following Meijer G-function
$$G_{1,3}^{3,0}\left(a^2\Bigg| \begin{array}{c} n+2 \\ -\dfrac{1}{2},1,\dfrac{3}{2} \\ \end{array} \right)$$
MeijerG[{{},{2+n}},{{-(1/2),1,3/2},{}},a^2]
be expressed more explicitly in terms of other special functions, but involving no infinite integrals?
$a\;$ is positive real number and $\;n=0,1,2\;$ is an integer.