What is the formula for the $n$th order derivative Gaussian wavelet?
A Gaussian wavelet is given by $$\psi(t) = C \exp(-\frac{(t-\mu)^2}{2\sigma})$$
with $\mu$ and $\sigma$ the mean and standard deviation of the Gaussian and $C$ chosen such that $||\psi(t)^2|| = 1$. This involves $C = \frac{1}{\sigma\sqrt{2\pi}}$ .
I can calculate the $n$th order derivative of the Gaussian wavelet function by hand. But in order to be a wavelet again, the constant $C_n$ should fulfill the condition $||\frac{\delta^n}{\delta t^n}\psi(t)^2|| = 1$.
How to calculate this normalization factor?