Formula:3794

Digital Library of Mathematical Functions ID 10.9.E26

${\displaystyle{\displaystyle J_{\mu}\left(z\right)J_{\nu}\left(z\right)=\frac{2}{\pi}\int_{0}^{\pi/2}J_{\mu+\nu}\left(2z\cos\theta\right)\cos\left((\mu-\nu)\theta\right)\mathrm{d}\theta,}}$

Constraint(s)

${\displaystyle{\displaystyle\Re(\mu+\nu)>-1}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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