Formula:653

Digital Library of Mathematical Functions ID 1.17.E24

${\displaystyle{\displaystyle\delta\left(x-a\right)=\frac{e^{-(x^{2}+a^{2})/2}}{\sqrt{\pi}}\sum_{k=0}^{\infty}\frac{H_{k}\left(x\right)H_{k}\left(a\right)}{2^{k}k!}.}}$

Symbols List

• ${\displaystyle{\displaystyle\delta\left(\NVar{x-a}\right)}}$:
• ${\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}$: Hermite polynomial
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle k}}$: integer
 

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