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DLMF:18.18.E37 - MaRDI portal

DLMF:18.18.E37 (Q6524)

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DLMF:18.18.E37
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    Statements

    DLMF defining formula
    ∑ ℓ = 0 n L ℓ ( α ) ⁡ ( x ) = L n ( α + 1 ) ⁡ ( x ) , superscript subscript ℓ 0 𝑛 Laguerre-polynomial-L 𝛼 ℓ 𝑥 Laguerre-polynomial-L 𝛼 1 𝑛 𝑥 {\displaystyle{\displaystyle\sum_{\ell=0}^{n}L^{(\alpha)}_{\ell}\left(x\right)% =L^{(\alpha+1)}_{n}\left(x\right),}}
    0 references
    Symbols used
    Laguerre (or generalized Laguerre) polynomial
    DLMF 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.m2agdec
    0 references
    nonnegative integer
    DLMF defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1xdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ajdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1afdec
    0 references
     
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