Formula:4172

Digital Library of Mathematical Functions ID 10.23.E21

${\displaystyle{\displaystyle x^{\nu}=\sum_{m=1}^{\infty}\frac{2J_{\nu}\left(j_{\nu,m}x\right)}{j_{\nu,m}J_{\nu+1}\left(j_{\nu,m}\right)},}}$

Constraint(s)

${\displaystyle{\displaystyle\nu>0,0\leq x<1}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle j_{\NVar{\nu},\NVar{m}}}}$:
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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