DLMF:3.5.E46 (Q1302): Difference between revisions

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Property / constraint
 

x 𝑥 {\displaystyle{\displaystyle x\in\mathbb{R}}}

x\in\Reals
Property / constraint: x 𝑥 {\displaystyle{\displaystyle x\in\mathbb{R}}} / rank
 
Normal rank

Revision as of 15:57, 30 December 2019

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DLMF:3.5.E46
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    Statements

    f ( x ) = 1 π - f ( t ) t - x d t , Hilbert-transform 𝑓 𝑥 1 superscript subscript principal-value-integral 𝑓 𝑡 𝑡 𝑥 𝑡 {\displaystyle{\displaystyle\mathcal{H}\mskip-3.0mu f\mskip 3.0mu \left(x% \right)=\frac{1}{\pi}\pvint_{-\infty}^{\infty}\frac{f(t)}{t-x}\mathrm{d}t,}}
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    x 𝑥 {\displaystyle{\displaystyle x\in\mathbb{R}}}
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