DLMF:18.23.E4 (Q5905)

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DLMF:18.23.E4
No description defined

    Statements

    Defining formula
    ( 1 - z c ) x ⁢ ( 1 - z ) - x - β = ∑ n = 0 ∞ ( β ) n n ! ⁢ M n ⁡ ( x ; β , c ) ⁢ z n , superscript 1 𝑧 𝑐 𝑥 superscript 1 𝑧 𝑥 𝛽 superscript subscript 𝑛 0 Pochhammer 𝛽 𝑛 𝑛 Meixner-polynomial-M 𝑛 𝑥 𝛽 𝑐 superscript 𝑧 𝑛 {\displaystyle{\displaystyle\left(1-\frac{z}{c}\right)^{x}(1-z)^{-x-\beta}=% \sum_{n=0}^{\infty}\frac{{\left(\beta\right)_{n}}}{n!}M_{n}\left(x;\beta,c% \right)z^{n},}}
    0 references
    DLMF id
    DLMF:18.23.E4
    0 references
    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    0 references
    Symbols used
    Q11663
    Defining formula
    M n ⁡ ( x ; β , c ) Meixner-polynomial-M 𝑛 𝑥 𝛽 𝑐 {\displaystyle{\displaystyle M_{\NVar{n}}\left(\NVar{x};\NVar{\beta},\NVar{c}% \right)}}
    xml-id
    C18.S19.T1.t1.r4.m2adec
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    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1abdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    Q11750
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1cdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1cdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1cdec
    0 references
     
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