Can this exponential function be represented in terms of the Meijer-G or Fox-H functions?

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For those who are experts with special functions, I was wondering if the exponential function given below can be represented in terms of the Meijer-G, Fox-H or any other special function.

$\gamma$ is a real number greater than or equal to zero, and k is positive real number.

$$\exp\left({-\ln^2 (\gamma^k)} \right)$$

Thanks