DLMF:4.7.E4 (Q1580)

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DLMF:4.7.E4
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    Statements

    Defining formula
    d n d z n ⁡ Ln ⁡ z = ( - 1 ) n - 1 ⁢ ( n - 1 ) ! ⁢ z - n . derivative 𝑧 𝑛 multivalued-natural-logarithm 𝑧 superscript 1 𝑛 1 𝑛 1 superscript 𝑧 𝑛 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}% \operatorname{Ln}z=(-1)^{n-1}(n-1)!z^{-n}.}}
    0 references
    DLMF id
    DLMF:4.7.E4
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    Symbols used
    derivative of $$f$$ with respect to $$x$$
    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.m2acdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
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    general logarithm function
    Defining formula
    Ln ⁡ z multivalued-natural-logarithm 𝑧 {\displaystyle{\displaystyle\operatorname{Ln}\NVar{z}}}
    xml-id
    C4.S2.E1.m2aadec
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