 Probabilists' Hermite polynomial

ID: probabilists-hermite-polynomial

The probabilists' Hermite polynomials are

He_{n} (x) = (- 1)^{n} e^{x^{2} /2} \frac{d ^{n}}{d x ^{n}} e^{- x^{2} /2} .

They are orthogonal for the standard Gaussian weight and satisfy

He_{n + 1} = x He_{n} - n He_{n - 1}

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