DLMF:1.16.E38 (Q646)

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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}}
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    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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