DLMF:1.9.E30 (Q305)

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DLMF:1.9.E30
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    Statements

    Defining formula
    f ⁢ ( z 0 ) = 1 2 ⁢ π ⁢ i ⁢ ∫ C f ⁢ ( z ) z - z 0 ⁢ d z , 𝑓 subscript 𝑧 0 1 2 𝜋 𝑖 subscript 𝐶 𝑓 𝑧 𝑧 subscript 𝑧 0 𝑧 {\displaystyle{\displaystyle f(z_{0})=\frac{1}{2\pi i}\int_{C}\frac{f(z)}{z-z_% {0}}\mathrm{d}z,}}
    0 references
    DLMF id
    DLMF:1.9.E30
    0 references
    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
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ajdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    Q10821
    Defining formula
    C 𝐶 {\displaystyle{\displaystyle C}}
    xml-id
    C1.S9.XMD12.m1bdec
    0 references
     
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