Question: The first four Hermite polynomials are 1, 2t, - 2 + 4t 2 , and -12t + 8t 3 . These polynomials arise naturally in

The first four Hermite polynomials are 1, 2t, - 2 + 4t², and -12t + 8t³. These polynomials arise naturally in the study of certain important differential equations in mathematical physics. Show that the first four Hermite polynomials form a basis of P₃.

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