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
Property / Symbols used
 
Property / Symbols used: Q10895 / rank
 
Normal rank
Property / Symbols used: Q10895 / qualifier
 
test:

( f ) ( x ) Hilbert-transform 𝑓 𝑥 {\displaystyle{\displaystyle\mathcal{H}\left(\NVar{f}\right)\left(\NVar{x}% \right)}}

\Hilberttrans@{\NVar{f}}@{\NVar{x}}
Property / Symbols used: Q10895 / qualifier
 
xml-id: C1.S14.SS5.p1.m2adec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aldec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1ardec
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
test:

{\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2adec
Property / Symbols used
 
Property / Symbols used: Cauchy principal value / rank
 
Normal rank
Property / Symbols used: Cauchy principal value / qualifier
 
test:

a b superscript subscript principal-value-integral 𝑎 𝑏 {\displaystyle{\displaystyle\pvint_{\NVar{a}}^{\NVar{b}}}}

\pvint_{\NVar{a}}^{\NVar{b}}
Property / Symbols used: Cauchy principal value / qualifier
 
xml-id: C1.S4.E24.m2adec
Property / Symbols used
 
Property / Symbols used: Q10812 / rank
 
Normal rank
Property / Symbols used: Q10812 / qualifier
 
test:

{\displaystyle{\displaystyle\mathbb{R}}}

\Reals
Property / Symbols used: Q10812 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r14.m2adec

Latest revision as of 16:53, 1 January 2020

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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,}}
    0 references
    0 references
    x 𝑥 {\displaystyle{\displaystyle x\in\mathbb{R}}}
    0 references
    ( f ) ( x ) Hilbert-transform 𝑓 𝑥 {\displaystyle{\displaystyle\mathcal{H}\left(\NVar{f}\right)\left(\NVar{x}% \right)}}
    C1.S14.SS5.p1.m2adec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aldec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1ardec
    0 references
    {\displaystyle{\displaystyle\in}}
    introduction.Sx4.p1.t1.r10.m2adec
    0 references
    a b superscript subscript principal-value-integral 𝑎 𝑏 {\displaystyle{\displaystyle\pvint_{\NVar{a}}^{\NVar{b}}}}
    C1.S4.E24.m2adec
    0 references
    {\displaystyle{\displaystyle\mathbb{R}}}
    introduction.Sx4.p2.t1.r14.m2adec
    0 references