DLMF:15.9.E9 (Q5099)

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DLMF:15.9.E9
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    Statements

    Defining formula
    M n ⁡ ( x ; β , c ) = F ⁡ ( - n , - x β ; 1 - 1 c ) . Meixner-polynomial-M 𝑛 𝑥 𝛽 𝑐 Gauss-hypergeometric-F 𝑛 𝑥 𝛽 1 1 𝑐 {\displaystyle{\displaystyle M_{n}\left(x;\beta,c\right)=F\left({-n,-x\atop% \beta};1-\frac{1}{c}\right).}}
    0 references
    DLMF id
    DLMF:15.9.E9
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    Defining formula
    F ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    xml-id
    C15.S2.E1.m2ahdec
    0 references
    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
    0 references
    Q11649
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C15.S1.XMD1.m1gdec
    0 references
    Q11650
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C15.S1.XMD10.m1hdec
    0 references
    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1dec
    0 references
     
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