DLMF:18.12.E13 (Q5655)

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DLMF:18.12.E13
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    Statements

    Defining formula
    ( 1 - z ) - α - 1 ⁢ exp ⁡ ( x ⁢ z z - 1 ) = ∑ n = 0 ∞ L n ( α ) ⁡ ( x ) ⁢ z n , superscript 1 𝑧 𝛼 1 𝑥 𝑧 𝑧 1 superscript subscript 𝑛 0 Laguerre-polynomial-L 𝛼 𝑛 𝑥 superscript 𝑧 𝑛 {\displaystyle{\displaystyle(1-z)^{-\alpha-1}\exp\left(\frac{xz}{z-1}\right)=% \sum_{n=0}^{\infty}L^{(\alpha)}_{n}\left(x\right)z^{n},}}
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    DLMF id
    DLMF:18.12.E13
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    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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    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.m2adec
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    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
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    Q11750
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1ldec
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    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ldec
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    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1kdec
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