DLMF:1.10.E10 (Q335)

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DLMF:1.10.E10
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    Statements

    DLMF 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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    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.m2acdec
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    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
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    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
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    variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C1.S1.XMD1.m1hdec
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    closed contour
    DLMF defining formula
    C 𝐶 {\displaystyle{\displaystyle C}}
    xml-id
    C1.S10.XMD5.m1bdec
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    Identifiers

     
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