Mathematics, 07.04.2021 04:40, lovedebrap11ih4

(a) 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.(b) The first four Laguerre polynomials are 1,1−t,2−4t+t2, and 6−18t+9t2−t3. Show that these four Laguerre polynomials form a basis of P3.

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(a) The first four Hermite polynomials are 1,2t,−2+4t2, and −12t+8t3. These polynomials arise natura...