Formula:4158

Digital Library of Mathematical Functions ID 10.23.E7

${\displaystyle{\displaystyle\mathscr{C}_{\nu}\left(w\right)\selection{\cos\\ \sin}(\nu\chi)=\sum_{k=-\infty}^{\infty}\mathscr{C}_{\nu+k}\left(u\right)J_{k}\left(v\right)\selection{\cos\\ \sin}(k\alpha),}}$

Constraint(s)

${\displaystyle{\displaystyle|ve^{\pm i\alpha}|<|u|}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: cylinder function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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