Formula:6285

Digital Library of Mathematical Functions ID 18.7.E20

${\displaystyle{\displaystyle H_{2n+1}\left(x\right)=(-1)^{n}2^{2n+1}n!\,xL^{(\frac{1}{2})}_{n}\left(x^{2}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}$: Hermite polynomial
• ${\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}\right)}}$: Laguerre (or generalized Laguerre) polynomial
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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