Formula:4345

Digital Library of Mathematical Functions ID 10.44.E1

${\displaystyle{\displaystyle\mathscr{Z}_{\nu}\left(\lambda z\right)=\lambda^{\pm\nu}\sum_{k=0}^{\infty}\frac{(\lambda^{2}-1)^{k}(\frac{1}{2}z)^{k}}{k!}\mathscr{Z}_{\nu\pm k}\left(z\right),}}$

Constraint(s)

${\displaystyle{\displaystyle|\lambda^{2}-1|<1}}$

Symbols List

• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\mathscr{Z}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified cylinder function
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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