Formula:6442

Digital Library of Mathematical Functions ID 18.17.E4

${\displaystyle{\displaystyle\int_{0}^{x}e^{-y^{2}}H_{n}\left(y\right)\mathrm{d}y=H_{n-1}\left(0\right)-e^{-x^{2}}H_{n-1}\left(x\right).}}$

Symbols List

• ${\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}$: Hermite polynomial
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle y}}$: real variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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