J ν ′ ( j ν , m ) ∼ ( − 1 ) m ( 2 / ν ) 2 3 π M ( a m ) ∑ k = 0 ∞ β k ν 2 k / 3 J_{\nu}'\left(j_{\nu,m}\right)\sim(-1)^{m}\frac{(2/\nu)^{\frac{2}{3}}}{\pi M\left(a_{m}\right)}\sum_{k=0}^{\infty}\frac{\beta_{k}}{\nu^{2k/3}}