DLMF:18.12.E13 (Q5655)

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DLMF:18.12.E13
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    Statements

    test
    ( 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},}}
    0 references
    DLMF id
    DLMF:18.12.E13
    0 references
    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    0 references
    Symbols used
    Q11333
    test
    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
    0 references
    exponential function
    test
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
     
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