DLMF:1.15.E39 (Q581)

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DLMF:1.15.E39
No description defined

    Statements

    Defining formula
    Φ ⁢ ( z ) = Φ ⁢ ( x + i ⁢ y ) = i π ⁢ ∫ - ∞ ∞ f ⁢ ( t ) ⁢ 1 ( x - t ) + i ⁢ y ⁢ d t , Φ 𝑧 Φ 𝑥 𝑖 𝑦 𝑖 𝜋 subscript superscript 𝑓 𝑡 1 𝑥 𝑡 𝑖 𝑦 𝑡 {\displaystyle{\displaystyle\Phi(z)=\Phi(x+iy)=\frac{i}{\pi}\int^{\infty}_{-% \infty}f(t)\frac{1}{(x-t)+iy}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:1.15.E39
    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.m2ahdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1andec
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    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.m3andec
    0 references
    Q10760
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C1.S1.XMD1.m1adec
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    Q10900
    Defining formula
    Φ ⁢ ( z ) Φ 𝑧 {\displaystyle{\displaystyle\Phi(z)}}
    xml-id
    C1.S15.XMD9.m1dec
    0 references
     
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