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

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ν > - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}

\realpart@@{\nu}>-\tfrac{1}{2}
Property / constraint: ν > - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}} / rank
 
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Revision as of 17:16, 30 December 2019

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DLMF:10.9.E27
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    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,}}
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    DLMF:10.9.E27
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    ν > - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}
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