Jν′⁡(z)∼-(2π⁢z)12⁢(sin⁡ω⁢∑k=0∞(-1)k⁢b2⁢k⁡(ν)z2⁢k+cos⁡ω⁢∑k=0∞(-1)k⁢b2⁢k+1⁡(ν)z2⁢k+1),