Mathematics, 14.04.2020 17:59 Sep101

The first five Hermite polynomials are 1, 2t, −2 + 4t 2 , −12t + 8t 3 , and 12 − 48t 2 + 16t 4 . These polynomials arise naturally in the study of certain important differential equations in mathematical physics. Show that the first five Hermite polynomials form a basis of P4.

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The first five Hermite polynomials are 1, 2t, −2 + 4t 2 , −12t + 8t 3 , and 12 − 48t 2 + 16t 4 . The...