DLMF:18.5.E12 (Q5520)

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DLMF:18.5.E12
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    L n ( α ) ( x ) = = 0 n ( α + + 1 ) n - ( n - ) ! ! ( - x ) = ( α + 1 ) n n ! F 1 1 ( - n α + 1 ; x ) . Laguerre-polynomial-L 𝛼 𝑛 𝑥 superscript subscript 0 𝑛 Pochhammer 𝛼 1 𝑛 𝑛 superscript 𝑥 Pochhammer 𝛼 1 𝑛 𝑛 Kummer-confluent-hypergeometric-M-as-1F1 𝑛 𝛼 1 𝑥 {\displaystyle{\displaystyle L^{(\alpha)}_{n}\left(x\right)=\sum_{\ell=0}^{n}% \frac{{\left(\alpha+\ell+1\right)_{n-\ell}}}{(n-\ell)!\;\ell!}(-x)^{\ell}=% \frac{{\left(\alpha+1\right)_{n}}}{n!}{{}_{1}F_{1}}\left({-n\atop\alpha+1};x% \right).}}
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    DLMF:18.5.E12
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