The Hermite polynomials Hn(x) are polynomial solutions to

Chapter 8, Problem 37E

(choose chapter or problem)

The Hermite polynomials are polynomial  \(H_{n}(\chi)\) solutions to Hermite’s equation

\(Y^{\prime \prime}-2 x y^{\prime}+2 n y=0\)

The Hermite polynomials are generated by

\(e^{2 t x-t 2}=\sum_{n=0}^{\infty} \frac{H_{n}(x)}{n !} t^{n}\)

Equation Transcription:

Text Transcription:

H_n(\chi)

Y''-2xy'+2ny=0

e^2 t x-t 2=\sum_n=0^\infty \fracH_n(x)n ! t^n

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