Formula:4151

Digital Library of Mathematical Functions ID 10.23.E2

${\displaystyle{\displaystyle\mathscr{C}_{\nu}\left(u\pm v\right)=\sum_{k=-\infty}^{\infty}\mathscr{C}_{\nu\mp k}\left(u\right)J_{k}\left(v\right),}}$

Constraint(s)

${\displaystyle{\displaystyle|v|<|u|}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: cylinder function
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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