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}}}