DLMF:1.17.E9 (Q668): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q10916 / rank
 
Normal rank
Property / Symbols used: Q10916 / qualifier
 
Defining formula:

ϕ ( x ) italic-ϕ 𝑥 {\displaystyle{\displaystyle\phi(x)}}

\phi(x)
Property / Symbols used: Q10916 / qualifier
 
xml-id: C1.S17.XMD1.m1edec

Latest revision as of 16:43, 1 January 2020

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DLMF:1.17.E9
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    Statements

    - ( 1 2 π - e i ( x - a ) t d t ) ϕ ( x ) d x = ϕ ( a ) . superscript subscript 1 2 𝜋 superscript subscript superscript 𝑒 𝑖 𝑥 𝑎 𝑡 𝑡 italic-ϕ 𝑥 𝑥 italic-ϕ 𝑎 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}\left(\frac{1}{2\pi}\int_{-% \infty}^{\infty}e^{i(x-a)t}\mathrm{d}t\right)\phi(x)\mathrm{d}x=\phi(a).}}
    0 references
    DLMF:1.17.E9
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2addec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aedec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2addec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aadec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aedec
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    ϕ ( x ) italic-ϕ 𝑥 {\displaystyle{\displaystyle\phi(x)}}
    C1.S17.XMD1.m1edec
    0 references