2.10.E26 (Q984)

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2.10.E26
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    Statements

    DLMF defining formula
    f n = 1 2 ⁢ π ⁢ i ⁢ ∫ 𝒞 f ⁢ ( z ) z n + 1 ⁢ d z , subscript 𝑓 𝑛 1 2 𝜋 𝑖 subscript 𝒞 𝑓 𝑧 superscript 𝑧 𝑛 1 𝑧 {\displaystyle{\displaystyle f_{n}=\frac{1}{2\pi i}\int_{\mathscr{C}}\frac{f(z% )}{z^{n+1}}\mathrm{d}z,}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
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    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
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    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ajdec
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    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
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    analytic function
    DLMF defining formula
    f ⁢ ( x ) 𝑓 𝑥 {\displaystyle{\displaystyle f(x)}}
    xml-id
    C2.S10.XMD13.m1adec
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    coefficients
    DLMF defining formula
    f n subscript 𝑓 𝑛 {\displaystyle{\displaystyle f_{n}}}
    xml-id
    C2.S10.XMD14.m1adec
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    simple closed contour
    DLMF defining formula
    𝒞 𝒞 {\displaystyle{\displaystyle\mathscr{C}}}
    xml-id
    C2.S10.XMD16.m1dec
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