If we consider a complex Gaussian random variable as $h\sim\mathcal{CN}(0,\gamma)$, where $\gamma$ is the variance. Is there any close form solution with $\gamma$ for $\mathbf{E}\left[\frac{1}{\|h\|_2^2}\right]$? where $\|\cdot\|^2$ denotes the norm-$2$ operation.

Really appreciate for any comments!

If we consider a complex Gaussian random variable as $h\sim\mathcal{CN}(0,\gamma)$, where $\gamma$ is the variance. Is there any closed-form solution with $\gamma$ for $\mathbf{E}\left[\frac{1}{\lVert h\rVert_2^2}\right]$? where $\lVert\cdot\rVert^2$ denotes the norm-$2$ operation.

Really appreciate for any comments!

If we consider a complex Gaussian random variable as $h\sim\mathcal{CN}(0,\gamma)$, where $\gamma$ is the variance. Is there any close form solution with $\gamma$ for $\mathbf{E}\left[\frac{1}{||h||_2^2}\right]$? where $||\cdot||^2$ denotes the norm-2 operation.

Really appreciate for any comments!

If we consider a complex Gaussian random variable as $h\sim\mathcal{CN}(0,\gamma)$, where $\gamma$ is the variance. Is there any close form solution with $\gamma$ for $\mathbf{E}\left[\frac{1}{\|h\|_2^2}\right]$? where $\|\cdot\|^2$ denotes the norm-$2$ operation.

Really appreciate for any comments!