Formula:4103

Digital Library of Mathematical Functions ID 10.22.E32

${\displaystyle{\displaystyle\int_{0}^{x}J_{\nu}\left(t\right)J_{1-\nu}\left(x-t\right)\mathrm{d}t=J_{0}\left(x\right)-\cos x,}}$

Constraint(s)

${\displaystyle{\displaystyle-1<\Re\nu<2}}$

Symbols List

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

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