Formula:4348

Digital Library of Mathematical Functions ID 10.44.E3

${\displaystyle{\displaystyle\mathscr{Z}_{\nu}\left(u\pm v\right)=\sum_{k=-\infty}^{\infty}(\pm 1)^{k}\mathscr{Z}_{\nu+k}\left(u\right)I_{k}\left(v\right),}}$

Constraint(s)

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

Symbols List

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

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