What is the approximation for $n^{th}$ convolution power (n-fold convolution) $g(x)= \underbrace{p * p * p * \cdots * p * p}_n$ with respsect to $p(x)$, where $p(x)$ is a probability density function?
I have solved this problem for large $n$ since I can use central limit theorem and approximate $g(x)$ to a Gaussian. I am not sure how to find the answer for the general case. Is there an approximation for $n^{th}$ convolution power (n-fold convolution)? Read more about convolution power here.