(a) When is a nonnegative integer, Hermites differential

Chapter 6, Problem 6.1.159

(choose chapter or problem)

(a) When is a nonnegative integer, Hermites differential equation always possesses a polynomial solution of degree n. Use given in 51, to find polynomial solutions for and Then use to find polynomial solutions for and (b) A Hermite polynomial is defined to be the nth degree polynomial solution of Hermites equation multiplied by an appropriate constant so that the coefficient of in is Use the polynomial solutions in part (a) to show that the first six Hermite polynomials are

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