DLMF:1.10.E10 (Q365)

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DLMF:1.10.E10
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    Statements

    Defining formula
    1 2 ⁢ π ⁢ i ⁢ ∫ C z ⁢ f ′ ⁢ ( z ) f ⁢ ( z ) ⁢ d z = (sum of locations of zeros) - (sum of locations of poles) , 1 2 𝜋 𝑖 subscript 𝐶 𝑧 superscript 𝑓 ′ 𝑧 𝑓 𝑧 𝑧 (sum of locations of zeros) (sum of locations of poles) {\displaystyle{\displaystyle\frac{1}{2\pi i}\int_{C}\frac{zf^{\prime}(z)}{f(z)% }\mathrm{d}z=\mbox{(sum of locations of zeros)}-\mbox{(sum of locations of % poles)},}}
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    DLMF id
    DLMF:1.10.E10
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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.m2acdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
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