DLMF:1.15.E40 (Q582)

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DLMF:1.15.E40
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    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}}
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    DLMF id
    DLMF:1.15.E40
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