Word Count : 222

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### Solution: Rodrigue’s formula for Hermite polynomials is given by: \[ H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} \left( e^{-x^2} \right) \] #### Step 1: Compute \(H_3(x)\) using Rodrigue’s Formula For \(n = 3\), \[ H_3(x) = (-1)^3 e^{x^2} ___ ________ ________ ________ ______ _______ __________ _________.
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