DLMF:10.21.E16

MaRDI QIDQ3997

• Label: DLMF:10.21.E16

Digital Library of Mathematical Functions ID 10.21.E16

${\displaystyle{\displaystyle J_{\nu}'\left(z\right)=\frac{(\tfrac{1}{2}z)^{\nu-1}}{2\Gamma\left(\nu\right)}\prod_{k=1}^{\infty}\left(1-\frac{z^{2}}{{{j^{\prime}_{\nu,k}}^{\mspace{-16.0mu }2}}}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\nu>0}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle{j^{\prime}_{\NVar{\nu},\NVar{m}}}}}$:
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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