Formula:6319

Digital Library of Mathematical Functions ID 18.9.E26

${\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}x}\left(e^{-x^{2}}H_{n}\left(x\right)\right)=-e^{-x^{2}}H_{n+1}\left(x\right).}}$

Symbols List

• ${\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}$: Hermite polynomial
• ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$: derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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