DLMF:18.26.E17 (Q5947)

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DLMF:18.26.E17
No description defined

    Statements

    Defining formula
    Δ y ( R n ⁡ ( y ⁢ ( y + γ + δ + 1 ) ; γ , δ , N ) ) Δ y ( y ⁢ ( y + γ + δ + 1 ) ) = - n ( γ + 1 ) ⁢ N ⁢ R n - 1 ⁡ ( y ⁢ ( y + γ + δ + 2 ) ; γ + 1 , δ , N - 1 ) . forward-difference 𝑦 dual-Hahn-R 𝑛 𝑦 𝑦 𝛾 𝛿 1 𝛾 𝛿 𝑁 forward-difference 𝑦 𝑦 𝑦 𝛾 𝛿 1 𝑛 𝛾 1 𝑁 dual-Hahn-R 𝑛 1 𝑦 𝑦 𝛾 𝛿 2 𝛾 1 𝛿 𝑁 1 {\displaystyle{\displaystyle\frac{\Delta_{y}\left(R_{n}\left(y(y+\gamma+\delta% +1);\gamma,\delta,N\right)\right)}{\Delta_{y}\left(y(y+\gamma+\delta+1)\right)% }=-\frac{n}{(\gamma+1)N}\*R_{n-1}\left(y(y+\gamma+\delta+2);\gamma+1,\delta,N-% 1\right).}}
    0 references
    DLMF id
    DLMF:18.26.E17
    0 references
    Symbols used
    Q11769
    Defining formula
    R n ⁡ ( x ; γ , δ , N ) dual-Hahn-R 𝑛 𝑥 𝛾 𝛿 𝑁 {\displaystyle{\displaystyle R_{\NVar{n}}\left(\NVar{x};\NVar{\gamma},\NVar{% \delta},\NVar{N}\right)}}
    xml-id
    C18.S25.T1.t1.r5.m2addec
    0 references
    Q11097
    Defining formula
    Δ forward-difference {\displaystyle{\displaystyle\Delta}}
    xml-id
    C3.S6.SS1.p1.m2aadec
    0 references
    Q11743
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C18.S1.XMD1.m1gdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1odec
    0 references
    Q11736
    Defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C18.S1.XMD7.m1gdec
    0 references
    Q11754
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C18.S1.XMD8.m1edec
    0 references
     
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