DLMF:3.4.E18 (Q1222)

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DLMF:3.4.E18
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    Statements

    Defining formula
    1 k ! ⁢ f ( k ) ⁢ ( x 0 ) = 1 2 ⁢ π ⁢ r k ⁢ ∫ 0 2 ⁢ π f ⁢ ( x 0 + r ⁢ e i ⁢ θ ) ⁢ e - i ⁢ k ⁢ θ ⁢ d θ . 1 𝑘 superscript 𝑓 𝑘 subscript 𝑥 0 1 2 superscript 𝑟 𝑘 superscript subscript 0 2 𝑓 subscript 𝑥 0 𝑟 superscript 𝑒 𝑖 𝜃 superscript 𝑒 𝑖 𝑘 𝜃 𝜃 {\displaystyle{\displaystyle\frac{1}{k!}\,f^{(k)}(x_{0})=\frac{1}{2\pi r^{k}}% \int_{0}^{2\pi}f(x_{0}+re^{i\theta})e^{-ik\theta}\mathrm{d}\theta.}}
    0 references
    DLMF id
    DLMF:3.4.E18
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q11165
    Defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C3.S4.XMD4.m1dec
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