DLMF:18.18.E19 (Q5809)

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DLMF:18.18.E19
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    Statements

    Defining formula
    x n = ( α + 1 ) n ⁢ ∑ ℓ = 0 n ( - n ) ℓ ( α + 1 ) ℓ ⁢ L ℓ ( α ) ⁡ ( x ) . superscript 𝑥 𝑛 Pochhammer 𝛼 1 𝑛 superscript subscript ℓ 0 𝑛 Pochhammer 𝑛 ℓ Pochhammer 𝛼 1 ℓ Laguerre-polynomial-L 𝛼 ℓ 𝑥 {\displaystyle{\displaystyle x^{n}={\left(\alpha+1\right)_{n}}\sum_{\ell=0}^{n% }\frac{{\left(-n\right)_{\ell}}}{{\left(\alpha+1\right)_{\ell}}}L^{(\alpha)}_{% \ell}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.18.E19
    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.m2aedec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1agdec
    0 references
    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1idec
    0 references
     
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