DLMF:18.23.E1 (Q5902)

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DLMF:18.23.E1
No description defined

    Statements

    Defining formula
    F 1 1 ⁡ ( - x α + 1 ; - z ) ⁢ F 1 1 ⁡ ( x - N β + 1 ; z ) = ∑ n = 0 N ( - N ) n ( β + 1 ) n ⁢ n ! ⁢ Q n ⁡ ( x ; α , β , N ) ⁢ z n , Kummer-confluent-hypergeometric-M-as-1F1 𝑥 𝛼 1 𝑧 Kummer-confluent-hypergeometric-M-as-1F1 𝑥 𝑁 𝛽 1 𝑧 superscript subscript 𝑛 0 𝑁 Pochhammer 𝑁 𝑛 Pochhammer 𝛽 1 𝑛 𝑛 Hahn-polynomial-Q 𝑛 𝑥 𝛼 𝛽 𝑁 superscript 𝑧 𝑛 {\displaystyle{\displaystyle{{}_{1}F_{1}}\left({-x\atop\alpha+1};-z\right){{}_% {1}F_{1}}\left({x-N\atop\beta+1};z\right)=\sum_{n=0}^{N}\frac{{\left(-N\right)% _{n}}}{{\left(\beta+1\right)_{n}}n!}Q_{n}\left(x;\alpha,\beta,N\right)z^{n},}}
    0 references
    DLMF id
    DLMF:18.23.E1
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    constraint
    x = 0 , 1 , … , N 𝑥 0 1 … 𝑁 {\displaystyle{\displaystyle x=0,1,\dots,N}}
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    Symbols used
    Q11768
    Defining formula
    Q n ⁡ ( x ; α , β , N ) Hahn-polynomial-Q 𝑛 𝑥 𝛼 𝛽 𝑁 {\displaystyle{\displaystyle Q_{\NVar{n}}\left(\NVar{x};\NVar{\alpha},\NVar{% \beta},\NVar{N}\right)}}
    xml-id
    C18.S19.T1.t1.r2.m1adec
    0 references
    Q11384
    Defining formula
    F 1 1 ⁡ ( a ; b ; z ) Kummer-confluent-hypergeometric-M-as-1F1 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle{{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}% \right)}}
    xml-id
    C16.S2.m7adec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q11750
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1dec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1dec
    0 references
    Q11736
    Defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C18.S1.XMD7.m1dec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1dec
    0 references
     
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