DLMF:10.9.E27 (Q3097): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

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

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1azdec

Revision as of 15:17, 2 January 2020

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DLMF:10.9.E27
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    Statements

    Defining formula
    J ν ⁡ ( z ) ⁢ J ν ⁡ ( ζ ) = 2 π ⁢ ∫ 0 π / 2 J 2 ⁢ ν ⁡ ( 2 ⁢ ( z ⁢ ζ ) 1 2 ⁢ sin ⁡ θ ) ⁢ cos ⁡ ( ( z - ζ ) ⁢ cos ⁡ θ ) ⁢ d θ , Bessel-J 𝜈 𝑧 Bessel-J 𝜈 𝜁 2 𝜋 superscript subscript 0 𝜋 2 Bessel-J 2 𝜈 2 superscript 𝑧 𝜁 1 2 𝜃 𝑧 𝜁 𝜃 𝜃 {\displaystyle{\displaystyle J_{\nu}\left(z\right)J_{\nu}\left(\zeta\right)=% \frac{2}{\pi}\int_{0}^{\pi/2}J_{2\nu}\left(2(z\zeta)^{\frac{1}{2}}\sin\theta% \right)\cos\left((z-\zeta)\cos\theta\right)\mathrm{d}\theta,}}
    0 references
    DLMF id
    DLMF:10.9.E27
    0 references
    constraint
    ℜ ⁡ ν > - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2andec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2azdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2amdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1azdec
    0 references
     
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