The first four Hermite polynomials are 1, 2t, -2 + 4t2 and

Chapter 4, Problem 21E

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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.2 Show that the first four Hermite polynomials form a basis of .

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