The Hermite polynomials are orthogonal on the interval
Chapter 10, Problem 31E(choose chapter or problem)
The Hermite polynomials \(H_{n}(x)\) are orthogonal on the interval \((-\infty, \infty)\) with respect to the weight function \(W(x)=e^{-x^{2}}\). Verify this fact for the first three Hermite polynomials:
\(H_{0}(x) \equiv 1, \quad H_{1}(x)=2 x\)
\(H_{2}(x)=4 x^{2}-2\)
Equation Transcription:
Text Transcription:
H_n(x)
(-\infty, \infty)
W(x) = e^-x2
H_0(x)1, H_1(x)=2x
H_2(x)=4x^2-2
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