Formula:6526

Digital Library of Mathematical Functions ID 18.18.E39

${\displaystyle{\displaystyle\sum_{\ell=0}^{n}\genfrac{(}{)}{0.0pt}{}{n}{\ell}H_{\ell}\left(2^{\frac{1}{2}}x\right)H_{n-\ell}\left(2^{\frac{1}{2}}y\right)=2^{\frac{1}{2}n}H_{n}\left(x+y\right),}}$

Symbols List

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

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