Formula:4098

Digital Library of Mathematical Functions ID 10.22.E27

${\displaystyle{\displaystyle\int_{0}^{x}t{J_{\nu-1}^{2}}\left(t\right)\mathrm{d}t=2\sum_{k=0}^{\infty}(\nu+2k){J_{\nu+2k}^{2}}\left(x\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\Re\nu>0}}$

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
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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