DLMF:1.16.E38 (Q646): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10908 / rank
 
Normal rank
Property / Symbols used: Q10908 / qualifier
 
test:

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

\deltaDistribution[x]
Property / Symbols used: Q10908 / qualifier
 
xml-id: C1.S16.SS3.m1afdec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

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

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1afdec
Property / Symbols used
 
Property / Symbols used: Q10905 / rank
 
Normal rank
Property / Symbols used: Q10905 / qualifier
 
test:

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.m5apdec
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
 
test:

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.m2acdec
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
test:

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

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2ahdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2acdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

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

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2aedec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

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

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3afdec
Property / Symbols used
 
Property / Symbols used: Q10914 / rank
 
Normal rank
Property / Symbols used: Q10914 / qualifier
 
test:

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

\mathcal{T}
Property / Symbols used: Q10914 / qualifier
 
xml-id: C1.S16.XMD12.m1adec
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
 
test:

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.m1ddec

Latest revision as of 16:39, 1 January 2020

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DLMF:1.16.E38
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    Statements

    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \intinnerprod{\Fouriertransdist@{\deltaDistribution[]}}{\phi}=\intinnerprod{\deltaDistribution[]}{\mathscr{F}(\phi)}=\intinnerprod{\deltaDistribution[]}{\frac{1}{\sqrt{2\cpi}}\int^{\infty}_{-\infty}\phi(t)\expe^{\iunit xt}\diff{t}}=\frac{1}{\sqrt{2\cpi}}\int_{-\infty}^{\infty}\phi(t)\diff{t}=\frac{1}{\sqrt{2\cpi}}\intinnerprod{1}{\phi},}
    0 references
    DLMF id
    DLMF:1.16.E38
    0 references
    constraint
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi\in\mathcal{T}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    Q10908
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deltaDistribution[x]}
    xml-id
    C1.S16.SS3.m1afdec
    0 references
    Q10770
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \diff{\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
    0 references
    Q10905
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \intinnerprod{\NVar{\Lambda}}{\NVar{\phi}}}
    xml-id
    C1.S16.SS1.p5.m5apdec
    0 references
    Fourier transform of a tempered distribution
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fouriertransdist@{\NVar{u}}}
    xml-id
    C1.S16.E35.m2acdec
    0 references
    Q10784
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \in}
    xml-id
    introduction.Sx4.p1.t1.r10.m2ahdec
    0 references
    base of natural logarithm
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    imaginary unit
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}
    xml-id
    C1.S9.E1.m2aedec
    0 references
    Q10771
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int}
    xml-id
    C1.S4.SS4.m3afdec
    0 references
    Q10914
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathcal{T}}
    xml-id
    C1.S16.XMD12.m1adec
    0 references
    Fourier transform of a test function (locally)
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathscr{F}(\phi)}
    xml-id
    C1.S16.XMD15.m1ddec
    0 references
     
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