Formula:4104

Digital Library of Mathematical Functions ID 10.22.E33

${\displaystyle{\displaystyle\int_{0}^{x}J_{\nu}\left(t\right)J_{-\nu}\left(x-t\right)\mathrm{d}t=\sin x,}}$

Constraint(s)

${\displaystyle{\displaystyle|\Re\nu|<1}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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