Meijer G explicit form

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Can the following case of the Meijer G-function be expressed more explicitly (in terms of other special functions, but involving no infinite integrals)? $$G_{3,4}^{3,2}\left(z\left|\begin{smallmatrix}1,\frac{2}{3},\frac{2}{3}\\ \frac{5}{3},\frac{2}{3},\frac{5}{3},0\end{smallmatrix}\right.\right)$$