DLMF:1.17.E13 (Q672): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10915 / rank
 
Normal rank
Property / Symbols used: Q10915 / qualifier
 
test:

δ ⁡ ( x - a ) Dirac-delta 𝑥 𝑎 {\displaystyle{\displaystyle\delta\left(\NVar{x-a}\right)}}

\Diracdelta@{\NVar{x-a}}
Property / Symbols used: Q10915 / qualifier
 
xml-id: C1.S17.SS1.p1.m2addec
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.m1aidec
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.m3aidec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
test:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec

Latest revision as of 15:44, 1 January 2020

No description defined
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English
DLMF:1.17.E13
No description defined

    Statements

    test
    δ ⁡ ( x - a ) = x ⁢ ∫ 0 ∞ t ⁢ J ν ⁡ ( x ⁢ t ) ⁢ J ν ⁡ ( a ⁢ t ) ⁢ d t , Dirac-delta 𝑥 𝑎 𝑥 superscript subscript 0 𝑡 Bessel-J 𝜈 𝑥 𝑡 Bessel-J 𝜈 𝑎 𝑡 𝑡 {\displaystyle{\displaystyle\delta\left(x-a\right)=x\int_{0}^{\infty}tJ_{\nu}% \left(xt\right)J_{\nu}\left(at\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:1.17.E13
    0 references
    constraint
    ℜ ⁡ ν > - 1 𝜈 1 {\displaystyle{\displaystyle\Re\nu>-1}}
    0 references
    x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}
    0 references
    a > 0 𝑎 0 {\displaystyle{\displaystyle a>0}}
    0 references
    Symbols used
    Bessel function of the first kind
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2adec
    0 references
    Q10915
    test
    δ ⁡ ( x - a ) Dirac-delta 𝑥 𝑎 {\displaystyle{\displaystyle\delta\left(\NVar{x-a}\right)}}
    xml-id
    C1.S17.SS1.p1.m2addec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aidec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aidec
    0 references
    Q10811
    test
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
     
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