DLMF:1.10.E8 (Q363)

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DLMF:1.10.E8
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    Statements

    Defining formula
    1 2 ⁢ π ⁢ i ⁢ ∫ C f ⁢ ( z ) ⁢ d z = sum of the residues of  f ⁢ ( z )  within  C . 1 2 𝜋 𝑖 subscript 𝐶 𝑓 𝑧 𝑧 sum of the residues of  f ⁢ ( z )  within  C {\displaystyle{\displaystyle\frac{1}{2\pi i}\int_{C}f(z)\mathrm{d}z=\mbox{sum % of the residues of $f(z)$ within $C$}.}}
    0 references
    DLMF id
    DLMF:1.10.E8
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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.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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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
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