DLMF:1.15.E40 (Q582)

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DLMF:1.15.E40
No description defined

    Statements

    Defining formula
    ℑ ⁡ Φ ⁢ ( x + i ⁢ y ) = 1 π ⁢ ∫ - ∞ ∞ f ⁢ ( t ) ⁢ x - t ( x - t ) 2 + y 2 ⁢ d t Φ 𝑥 𝑖 𝑦 1 𝜋 subscript superscript 𝑓 𝑡 𝑥 𝑡 superscript 𝑥 𝑡 2 superscript 𝑦 2 𝑡 {\displaystyle{\displaystyle\Im\Phi(x+iy)=\frac{1}{\pi}\int^{\infty}_{-\infty}% f(t)\frac{x-t}{(x-t)^{2}+y^{2}}\mathrm{d}t}}
    0 references
    DLMF id
    DLMF:1.15.E40
    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.m2aidec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aodec
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    Q10901
    Defining formula
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2adec
    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.m3aodec
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    Q10900
    Defining formula
    Φ ⁢ ( z ) Φ 𝑧 {\displaystyle{\displaystyle\Phi(z)}}
    xml-id
    C1.S15.XMD9.m1adec
    0 references
     
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