J ν ′ ( z ) = ( 1 2 z ) ν − 1 2 Γ ( ν ) ∏ k = 1 ∞ ( 1 − z 2 j ν , k ′ 2 ) 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}}^{2}}}\right)