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Question: please solve all the parts for this question and give...

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Please solve all the parts for this question and give a detailed explanation for your answer. Please provide as much steps and explanation as possible. You have to use power series to solve this question.

The equation where λ is a constant is known at the Hermite equation. It is an important equation in mathe- matical physics a. Find the first four nonzero terms in each of two solutions about x and show that they form a fundamental set of solutions. b. Using your answer to part a, observe that if A is a nonnegative even integer, then one or the other series solutions terminates and becomes a polynomial. Find the polynomial solutions for λ 0, 2, 4, 6, 8, 10. c. The Hermite polynomial H ( is defined as the polynomial solution of the Hermite equation with λ = 2n for which the coefficients ofr is 2. Using your answer to part b) md Ho(x), H(x), ..., Hs(x)

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