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DLMF:18.5.E5 - MaRDI portal

DLMF:18.5.E5 (Q6210)

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DLMF:18.5.E5
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    Statements

    DLMF defining formula
    p n ⁢ ( x ) = 1 κ n ⁢ w ⁢ ( x ) ⁢ d n d x n ⁡ ( w ⁢ ( x ) ⁢ ( F ⁢ ( x ) ) n ) . subscript 𝑝 𝑛 𝑥 1 subscript 𝜅 𝑛 𝑤 𝑥 derivative 𝑥 𝑛 𝑤 𝑥 superscript 𝐹 𝑥 𝑛 {\displaystyle{\displaystyle p_{n}(x)=\frac{1}{\kappa_{n}w(x)}\frac{{\mathrm{d% }}^{n}}{{\mathrm{d}x}^{n}}\left(w(x)(F(x))^{n}\right).}}
    0 references
    Symbols used
    derivative of $$f$$ with respect to $$x$$
    DLMF defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2adec
    0 references
    weight function
    DLMF defining formula
    w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}
    xml-id
    C18.S1.XMD10.m1dec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ddec
    0 references
    polynomial of degree n
    DLMF defining formula
    p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    xml-id
    C18.S1.XMD9.m1dec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1ddec
    0 references

    Identifiers

     
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