DLMF:18.20.E1 (Q5841)

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DLMF:18.20.E1
No description defined

    Statements

    Defining formula
    p n ⁢ ( x ) = 1 κ n ⁢ w x ⁢ ∇ x n ( w x ⁢ ∏ ℓ = 0 n - 1 F ⁢ ( x + ℓ ) ) , subscript 𝑝 𝑛 𝑥 1 subscript 𝜅 𝑛 subscript 𝑤 𝑥 superscript backward-difference 𝑥 𝑛 subscript 𝑤 𝑥 superscript subscript product ℓ 0 𝑛 1 𝐹 𝑥 ℓ {\displaystyle{\displaystyle p_{n}(x)=\frac{1}{\kappa_{n}w_{x}}\nabla_{x}^{n}% \left(w_{x}\prod_{\ell=0}^{n-1}F(x+\ell)\right),}}
    0 references
    DLMF id
    DLMF:18.20.E1
    0 references
    constraint
    x ∈ X 𝑥 𝑋 {\displaystyle{\displaystyle x\in X}}
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    Symbols used
    Q11764
    Defining formula
    ∇ x backward-difference 𝑥 {\displaystyle{\displaystyle\nabla_{\NVar{x}}}}
    xml-id
    C18.S1.EGx2.m1adec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
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    Q11734
    Defining formula
    w x subscript 𝑤 𝑥 {\displaystyle{\displaystyle w_{x}}}
    xml-id
    C18.S1.XMD11.m1dec
    0 references
    Q11735
    Defining formula
    X 𝑋 {\displaystyle{\displaystyle X}}
    xml-id
    C18.S1.XMD12.m1dec
    0 references
    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1dec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1dec
    0 references
    Q11731
    Defining formula
    p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    xml-id
    C18.S1.XMD9.m1dec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1dec
    0 references
    Q11765
    Defining formula
    F ⁢ ( x ) 𝐹 𝑥 {\displaystyle{\displaystyle F(x)}}
    xml-id
    C18.S20.XMD1.m1dec
    0 references
    Q11766
    Defining formula
    κ n subscript 𝜅 𝑛 {\displaystyle{\displaystyle\kappa_{n}}}
    xml-id
    C18.S20.XMD2.m1dec
    0 references
     
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