DLMF:1.17.E11 (Q670): Difference between revisions

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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.m3agdec
Property / Symbols used
 
Property / Symbols used: Q10757 / rank
 
Normal rank
Property / Symbols used: Q10757 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q10757 / qualifier
 
xml-id: C1.S1.XMD7.m1fdec

Latest revision as of 16:44, 1 January 2020

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DLMF:1.17.E11
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    Statements

    Defining formula
    δ n ⁡ ( x - a ) = 1 2 ⁢ π ⁢ ∫ - ∞ ∞ e - t 2 / ( 4 ⁢ n ) ⁢ e i ⁢ ( x - a ) ⁢ t ⁢ d t , Dirac-delta-sequence 𝑛 𝑥 𝑎 1 2 𝜋 superscript subscript superscript 𝑒 superscript 𝑡 2 4 𝑛 superscript 𝑒 𝑖 𝑥 𝑎 𝑡 𝑡 {\displaystyle{\displaystyle\delta_{n}\left(x-a\right)=\frac{1}{2\pi}\int_{-% \infty}^{\infty}e^{-t^{2}/(4n)}e^{i(x-a)t}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:1.17.E11
    0 references
    Symbols used
    Q10917
    Defining formula
    δ n ⁡ ( x ) Dirac-delta-sequence 𝑛 𝑥 {\displaystyle{\displaystyle\delta_{n}\left(\NVar{x}\right)}}
    xml-id
    C1.S17.SS1.p1.m6acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
    0 references
    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1fdec
    0 references
     
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