DLMF:1.17.E21 (Q680): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2akdec
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.m2ahdec
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.m1cdec

Latest revision as of 16:45, 1 January 2020

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DLMF:1.17.E21
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    Statements

    δ ( x - a ) = 1 2 π k = - e i k ( x - a ) . Dirac-delta 𝑥 𝑎 1 2 𝜋 superscript subscript 𝑘 superscript 𝑒 𝑖 𝑘 𝑥 𝑎 {\displaystyle{\displaystyle\delta\left(x-a\right)=\frac{1}{2\pi}\sum_{k=-% \infty}^{\infty}e^{ik(x-a)}.}}
    0 references
    DLMF:1.17.E21
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    δ ( x - a ) Dirac-delta 𝑥 𝑎 {\displaystyle{\displaystyle\delta\left(\NVar{x-a}\right)}}
    C1.S17.SS1.p1.m2ahdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2amdec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2akdec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2ahdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C1.S1.XMD4.m1cdec
    0 references