DLMF:3.4.E17 (Q1221)

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DLMF:3.4.E17
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    Statements

    Defining formula
    1 k ! ⁢ f ( k ) ⁢ ( x 0 ) = 1 2 ⁢ π ⁢ i ⁢ ∫ C f ⁢ ( ζ ) ( ζ - x 0 ) k + 1 ⁢ d ζ , 1 𝑘 superscript 𝑓 𝑘 subscript 𝑥 0 1 2 𝑖 subscript 𝐶 𝑓 𝜁 superscript 𝜁 subscript 𝑥 0 𝑘 1 𝜁 {\displaystyle{\displaystyle\frac{1}{k!}\,f^{(k)}(x_{0})=\frac{1}{2\pi i}\int_% {C}\frac{f(\zeta)}{(\zeta-x_{0})^{k+1}}\,\mathrm{d}\zeta,}}
    0 references
    DLMF id
    DLMF:3.4.E17
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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