DLMF:1.17.E17 (Q676): 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: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\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
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3amdec
Property / Symbols used
 
Property / Symbols used: Q10756 / rank
 
Normal rank
Property / Symbols used: Q10756 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q10756 / qualifier
 
xml-id: C1.S1.XMD4.m1dec
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.m1fdec

Latest revision as of 16:45, 1 January 2020

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DLMF:1.17.E17
No description defined

    Statements

    1 2 π k = - e - i k a ( - π π ϕ ( x ) e i k x d x ) = ϕ ( a ) , 1 2 𝜋 superscript subscript 𝑘 superscript 𝑒 𝑖 𝑘 𝑎 superscript subscript 𝜋 𝜋 italic-ϕ 𝑥 superscript 𝑒 𝑖 𝑘 𝑥 𝑥 italic-ϕ 𝑎 {\displaystyle{\displaystyle\frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{-ika}% \left(\int_{-\pi}^{\pi}\phi(x)e^{ikx}\mathrm{d}x\right)=\phi(a),}}
    0 references
    DLMF:1.17.E17
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aidec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1amdec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2ahdec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aedec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3amdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C1.S1.XMD4.m1dec
    0 references
    ϕ ( x ) italic-ϕ 𝑥 {\displaystyle{\displaystyle\phi(x)}}
    C1.S17.XMD1.m1fdec
    0 references