Question: The first four Hermite polynomials are1, 2t, - 2 + 4t^2 and-12t +8t^3 . These polynomials arise naturally in the study of certain important differential

The first four Hermite polynomials are1, 2t, - 2 + 4t^2 and-12t +8t^3 . These polynomials arise naturally in the study of certain important differential equations in mathematical physics.³⁸Show that the first four Hermite polynomials form a basis of P2.

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