DLMF:18.23.E5 (Q5906)

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DLMF:18.23.E5
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    e z ( 1 - z a ) x = n = 0 C n ( x ; a ) n ! z n , superscript 𝑒 𝑧 superscript 1 𝑧 𝑎 𝑥 superscript subscript 𝑛 0 Charlier-polynomial-C 𝑛 𝑥 𝑎 𝑛 superscript 𝑧 𝑛 {\displaystyle{\displaystyle e^{z}\left(1-\frac{z}{a}\right)^{x}=\sum_{n=0}^{% \infty}\frac{C_{n}\left(x;a\right)}{n!}z^{n},}}
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    DLMF:18.23.E5
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    x = 0 , 1 , 2 , 𝑥 0 1 2 {\displaystyle{\displaystyle x=0,1,2,\dots}}
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    C n ( x ; a ) Charlier-polynomial-C 𝑛 𝑥 𝑎 {\displaystyle{\displaystyle C_{\NVar{n}}\left(\NVar{x};\NVar{a}\right)}}
    C18.S19.T1.t1.r5.m2adec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
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    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5acdec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C18.S1.XMD2.m1ddec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1ddec
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