DLMF:10.9.E28 (Q3098): Difference between revisions

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Property / constraint
 

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

\realpart@@{\nu}>-1
Property / constraint: ν > - 1 𝜈 1 {\displaystyle{\displaystyle\Re\nu>-1}} / rank
 
Normal rank

Revision as of 17:16, 30 December 2019

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DLMF:10.9.E28
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    Statements

    J ν ( z ) J ν ( ζ ) = 1 2 π i c - i c + i exp ( 1 2 t - z 2 + ζ 2 2 t ) I ν ( z ζ t ) d t t , Bessel-J 𝜈 𝑧 Bessel-J 𝜈 𝜁 1 2 𝜋 𝑖 superscript subscript 𝑐 𝑖 𝑐 𝑖 1 2 𝑡 superscript 𝑧 2 superscript 𝜁 2 2 𝑡 modified-Bessel-first-kind 𝜈 𝑧 𝜁 𝑡 𝑡 𝑡 {\displaystyle{\displaystyle J_{\nu}\left(z\right)J_{\nu}\left(\zeta\right)=% \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\*\exp\left(\frac{1}{2}t-\frac{z^{% 2}+\zeta^{2}}{2t}\right)I_{\nu}\left(\frac{z\zeta}{t}\right)\frac{\mathrm{d}t}% {t},}}
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    ν > - 1 𝜈 1 {\displaystyle{\displaystyle\Re\nu>-1}}
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