Formula:6460

Digital Library of Mathematical Functions ID 18.17.E22

${\displaystyle{\displaystyle\frac{1}{2\sqrt{\pi}}\int_{-\infty}^{\infty}e^{-\frac{1}{4}x^{2}}\mathit{He}_{n}\left(x\right)e^{\frac{1}{2}\mathrm{i}xy}\mathrm{d}x={\mathrm{i}^{n}}e^{-\frac{1}{4}y^{2}}\mathit{He}_{n}\left(y\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathit{He}_{\NVar{n}}\left(\NVar{x}\right)}}$: Hermite polynomial
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle y}}$: real variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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