Formula:6510

Digital Library of Mathematical Functions ID 18.18.E23

${\displaystyle{\displaystyle H_{m}\left(x\right)H_{n}\left(x\right)=\sum_{\ell=0}^{\min(m,n)}\genfrac{(}{)}{0.0pt}{}{m}{\ell}\genfrac{(}{)}{0.0pt}{}{n}{\ell}2^{\ell}\ell!H_{m+n-2\ell}\left(x\right).}}$

Symbols List

• ${\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}$: Hermite polynomial
• ${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\ell}}$: nonnegative integer
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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