Formula:6527

Digital Library of Mathematical Functions ID 18.18.E40

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

Symbols List

• ${\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}$: Hermite polynomial
• ${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle L_{\NVar{n}}\left(\NVar{x}\right)=L^{(0)}_{n}\left(x\right)}}$: Laguerre polynomial
• ${\displaystyle{\displaystyle y}}$: real variable
• ${\displaystyle{\displaystyle\ell}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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