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where denotes the Hermite polynomial.
The normalisation coefficient is given by:
The prefactor in the resolution of the identity of the continuous wavelet transform for this wavelet is given by:
i.e. Hermitian wavelets are admissible for all positive .
Examples of Hermitian wavelets: Starting from a Gaussian function with :
the first 3 derivatives read
and their norms
So the wavelets which are the negative normalized derivatives are: