Formula:6500

Digital Library of Mathematical Functions ID 18.18.E13

${\displaystyle{\displaystyle H_{n}\left(\lambda x\right)=\lambda^{n}\sum_{\ell=0}^{\left\lfloor n/2\right\rfloor}\frac{{\left(-n\right)_{2\ell}}}{\ell!}(1-\lambda^{-2})^{\ell}H_{n-2\ell}\left(x\right).}}$

Symbols List

• ${\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}$: Hermite polynomial
• ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$:
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}$:
• ${\displaystyle{\displaystyle\ell}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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