Formula:6499

Digital Library of Mathematical Functions ID 18.18.E12

${\displaystyle{\displaystyle\frac{L^{(\alpha)}_{n}\left(\lambda x\right)}{L^{(\alpha)}_{n}\left(0\right)}=\sum_{\ell=0}^{n}\genfrac{(}{)}{0.0pt}{}{n}{\ell}\lambda^{\ell}(1-\lambda)^{n-\ell}\frac{L^{(\alpha)}_{\ell}\left(x\right)}{L^{(\alpha)}_{\ell}\left(0\right)}.}}$

Symbols List

• ${\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}\right)}}$: Laguerre (or generalized Laguerre) polynomial
• ${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle\ell}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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