DLMF:18.18.E18 (Q5808)

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DLMF:18.18.E18
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    Statements

    Defining formula
    L n ( β ) ⁡ ( x ) = ∑ ℓ = 0 n ( β - α ) n - ℓ ( n - ℓ ) ! ⁢ L ℓ ( α ) ⁡ ( x ) , Laguerre-polynomial-L 𝛽 𝑛 𝑥 superscript subscript ℓ 0 𝑛 Pochhammer 𝛽 𝛼 𝑛 ℓ 𝑛 ℓ Laguerre-polynomial-L 𝛼 ℓ 𝑥 {\displaystyle{\displaystyle L^{(\beta)}_{n}\left(x\right)=\sum_{\ell=0}^{n}% \frac{{\left(\beta-\alpha\right)_{n-\ell}}}{(n-\ell)!}L^{(\alpha)}_{\ell}\left% (x\right),}}
    0 references
    DLMF id
    DLMF:18.18.E18
    0 references
    Symbols used
    Q11333
    Defining formula
    L n ( α ) ⁡ ( x ) Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r12.m2addec
    0 references
     
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