Formula:6461

Digital Library of Mathematical Functions ID 18.17.E23

${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-\frac{1}{2}x^{2}}\mathit{He}_{2n}\left(x\right)\cos\left(xy\right)\mathrm{d}x=(-1)^{n}\sqrt{\tfrac{1}{2}\pi}y^{2n}e^{-\frac{1}{2}y^{2}},}}$

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
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: 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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