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d-2-dx-2-2x-d-dx-2n-H-n-x-0-Determine-the-first-4-polynomials-of-Hermite-H-n-




Question Number 108022 by Ar Brandon last updated on 13/Aug/20
((d^2 /dx^2 )−2x(d/dx)+2n)H_n (x)=0  Determine the first-4 polynomials of Hermite(H_n )
$$\left(\frac{\mathrm{d}^{\mathrm{2}} }{\mathrm{dx}^{\mathrm{2}} }−\mathrm{2x}\frac{\mathrm{d}}{\mathrm{dx}}+\mathrm{2n}\right)\mathrm{H}_{\mathrm{n}} \left(\mathrm{x}\right)=\mathrm{0} \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{first}-\mathrm{4}\:\mathrm{polynomials}\:\mathrm{of}\:\mathrm{Hermite}\left(\mathrm{H}_{\mathrm{n}} \right) \\ $$

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