DLMF:1.17.E19 (Q678): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10917 / rank
 
Normal rank
Property / Symbols used: Q10917 / qualifier
 
test:

δ n ⁡ ( x ) Dirac-delta-sequence 𝑛 𝑥 {\displaystyle{\displaystyle\delta_{n}\left(\NVar{x}\right)}}

\Diracdeltaseq{n}@{\NVar{x}}
Property / Symbols used: Q10917 / qualifier
 
xml-id: C1.S17.SS1.p1.m6addec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2akdec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aodec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aodec
Property / Symbols used
 
Property / Symbols used: Q10757 / rank
 
Normal rank
Property / Symbols used: Q10757 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q10757 / qualifier
 
xml-id: C1.S1.XMD7.m1gdec
Property / Symbols used
 
Property / Symbols used: Q10916 / rank
 
Normal rank
Property / Symbols used: Q10916 / qualifier
 
test:

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

\phi(x)
Property / Symbols used: Q10916 / qualifier
 
xml-id: C1.S17.XMD1.m1hdec

Latest revision as of 15:45, 1 January 2020

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DLMF:1.17.E19
No description defined

    Statements

    test
    lim n → ∞ ⁡ ∫ - π π δ n ⁡ ( x - a ) ⁢ ϕ ⁢ ( x ) ⁢ d x = ϕ ⁢ ( a ) , subscript → 𝑛 superscript subscript 𝜋 𝜋 Dirac-delta-sequence 𝑛 𝑥 𝑎 italic-ϕ 𝑥 𝑥 italic-ϕ 𝑎 {\displaystyle{\displaystyle\lim_{n\to\infty}\int_{-\pi}^{\pi}\delta_{n}\left(% x-a\right)\phi(x)\mathrm{d}x=\phi(a),}}
    0 references
    DLMF id
    DLMF:1.17.E19
    0 references
    Symbols used
    Q10917
    test
    δ n ⁡ ( x ) Dirac-delta-sequence 𝑛 𝑥 {\displaystyle{\displaystyle\delta_{n}\left(\NVar{x}\right)}}
    xml-id
    C1.S17.SS1.p1.m6addec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2akdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aodec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aodec
    0 references
    Q10757
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1gdec
    0 references
    Q10916
    test
    ϕ ⁢ ( x ) italic-ϕ 𝑥 {\displaystyle{\displaystyle\phi(x)}}
    xml-id
    C1.S17.XMD1.m1hdec
    0 references
     
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