DLMF:1.9.E28 (Q303)

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DLMF:1.9.E28
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    Statements

    Defining formula
    ∫ C f ⁢ ( z ) ⁢ d z = ∫ a b f ⁢ ( z ⁢ ( t ) ) ⁢ ( x ′ ⁢ ( t ) + i ⁢ y ′ ⁢ ( t ) ) ⁢ d t , subscript 𝐶 𝑓 𝑧 𝑧 superscript subscript 𝑎 𝑏 𝑓 𝑧 𝑡 superscript 𝑥 ′ 𝑡 𝑖 superscript 𝑦 ′ 𝑡 𝑡 {\displaystyle{\displaystyle\int_{C}f(z)\mathrm{d}z=\int_{a}^{b}f(z(t))(x^{% \prime}(t)+iy^{\prime}(t))\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:1.9.E28
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aidec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
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