Question Bank MCQ • 1 Mark Section 1: Mathematical Physics Differential equations

QB_PH_024: Differential equations

Question Statement

The Hermite polynomial $H_2(x)$ generated by $e^{2tx - t^2} = \sum_{n=0}^\infty H_n(x) \frac{t^n}{n!}$ is:
(A) 4x^2 - 2
(B) 2x^2 - 1
(C) 4x^2 + 2
(D) 8x^3 - 12x
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $e^{2tx - t^2} = 1 + 2tx + (4x^2 - 2) t^2/2! + \dots$.
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