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\Psi_{n}(t)=(2n)^{- rac{n}{2}}c_{n}H_{n}\left( rac{t}{\sqrt{n}} ight)e^{- rac{1}{2n}t^{2}}

where H_{n}\left({x} ight) denotes the n^ extrm{th} Hermite Polynomial .

The normalisation coefficient c_{n} is given by:

c_{n} = \left(n^{ rac{1}{2}-n}\Gamma(n+ rac{1}{2}) ight)^{- rac{1}{2}} = \left(n^{ rac{1}{2}-n}\sqrt{\pi}2^{-n}(2n-1)!! ight)^{- rac{1}{2}}\quad n\in\mathbb{Z}

The prefactor C_{\Psi} in the resolution of the identity of the continuous wavelet transform for this wavelet is given by:

C_{\Psi}= rac{4\pi n}{2n-1}

i.e. Hermitian wavelets are admissible orall~n>0.