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Please help me in proving the following expression

\(\displaystyle H_{2n}(x)=(-1)^n2^{2n}n!L_n^{-\frac{1}{2}}(x^2)\)

where \(\displaystyle H_n\) is the Hermite polynomial and \(\displaystyle L_n^{-\frac{1}{2}}\) is the associated Laguerre polynomial.

\(\displaystyle H_{2n}(x)=(-1)^n2^{2n}n!L_n^{-\frac{1}{2}}(x^2)\)

where \(\displaystyle H_n\) is the Hermite polynomial and \(\displaystyle L_n^{-\frac{1}{2}}\) is the associated Laguerre polynomial.

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