DLMF:1.16.E41 (Q649): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10905 / rank
 
Normal rank
Property / Symbols used: Q10905 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \intinnerprod{\NVar{\Lambda}}{\NVar{\phi}}}

\intinnerprod{\NVar{\Lambda}}{\NVar{\phi}}
Property / Symbols used: Q10905 / qualifier
 
xml-id: C1.S16.SS1.p5.m5aqdec
Property / Symbols used
 
Property / Symbols used: Fourier transform of a tempered distribution / rank
 
Normal rank
Property / Symbols used: Fourier transform of a tempered distribution / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fouriertransdist@{\NVar{u}}}

\Fouriertransdist@{\NVar{u}}
Property / Symbols used: Fourier transform of a tempered distribution / qualifier
 
xml-id: C1.S16.E35.m2aedec
Property / Symbols used
 
Property / Symbols used: Fourier transform of a test function (locally) / rank
 
Normal rank
Property / Symbols used: Fourier transform of a test function (locally) / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathscr{F}(\phi)}

\mathscr{F}(\phi)
Property / Symbols used: Fourier transform of a test function (locally) / qualifier
 
xml-id: C1.S16.XMD15.m1edec
Property / Symbols used
 
Property / Symbols used: Q10910 / rank
 
Normal rank
Property / Symbols used: Q10910 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(x)}

\phi(x)
Property / Symbols used: Q10910 / qualifier
 
xml-id: C1.S16.XMD7.m1cdec

Latest revision as of 15:40, 1 January 2020

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DLMF:1.16.E41
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    Statements

    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \intinnerprod{\Fouriertransdist@{1}}{\phi}=\sqrt{2\cpi}\intinnerprod{\Fouriertransdist@{\Fouriertransdist@{\deltaDistribution[]}}}{\phi}=\sqrt{2\cpi}\intinnerprod{\Fouriertransdist@{\deltaDistribution[]}}{\mathscr{F}(\phi)}=\sqrt{2\cpi}\intinnerprod{\deltaDistribution[]}{\mathscr{F}(\mathscr{F}(\phi))}=\sqrt{2\cpi}\intinnerprod{\deltaDistribution[]}{\phi_{-}}=\sqrt{2\cpi}\phi(0),}
    0 references
    DLMF:1.16.E41
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi}
    C3.S12.E1.m2aedec
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deltaDistribution[x]}
    C1.S16.SS3.m1ahdec
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \intinnerprod{\NVar{\Lambda}}{\NVar{\phi}}}
    C1.S16.SS1.p5.m5aqdec
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fouriertransdist@{\NVar{u}}}
    C1.S16.E35.m2aedec
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathscr{F}(\phi)}
    C1.S16.XMD15.m1edec
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(x)}
    C1.S16.XMD7.m1cdec
    0 references