DLMF:10.9.E26 (Q3096): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
test:

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2aldec

Revision as of 14:17, 2 January 2020

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DLMF:10.9.E26
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    Statements

    test
    J μ ⁡ ( z ) ⁢ J ν ⁡ ( z ) = 2 π ⁢ ∫ 0 π / 2 J μ + ν ⁡ ( 2 ⁢ z ⁢ cos ⁡ θ ) ⁢ cos ⁡ ( ( μ - ν ) ⁢ θ ) ⁢ d θ , Bessel-J 𝜇 𝑧 Bessel-J 𝜈 𝑧 2 𝜋 superscript subscript 0 𝜋 2 Bessel-J 𝜇 𝜈 2 𝑧 𝜃 𝜇 𝜈 𝜃 𝜃 {\displaystyle{\displaystyle J_{\mu}\left(z\right)J_{\nu}\left(z\right)=\frac{% 2}{\pi}\int_{0}^{\pi/2}J_{\mu+\nu}\left(2z\cos\theta\right)\cos\left((\mu-\nu)% \theta\right)\mathrm{d}\theta,}}
    0 references
    DLMF id
    DLMF:10.9.E26
    0 references
    constraint
    ℜ ⁡ ( μ + ν ) > - 1 𝜇 𝜈 1 {\displaystyle{\displaystyle\Re(\mu+\nu)>-1}}
    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.m2amdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aydec
    0 references
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aldec
    0 references
     
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