DLMF:10.17.E9 (Q3178)

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DLMF:10.17.E9
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    J ν ′ ⁡ ( z ) ∼ - ( 2 π ⁢ z ) 1 2 ⁢ ( sin ⁡ ω ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ b 2 ⁢ k ⁢ ( ν ) z 2 ⁢ k + cos ⁡ ω ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ b 2 ⁢ k + 1 ⁢ ( ν ) z 2 ⁢ k + 1 ) , asymptotic-expansion diffop Bessel-J 𝜈 1 𝑧 superscript 2 𝜋 𝑧 1 2 𝜔 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑏 2 𝑘 𝜈 superscript 𝑧 2 𝑘 𝜔 superscript subscript 𝑘 0 superscript 1 𝑘 subscript 𝑏 2 𝑘 1 𝜈 superscript 𝑧 2 𝑘 1 {\displaystyle{\displaystyle J_{\nu}'\left(z\right)\sim-\left(\frac{2}{\pi z}% \right)^{\frac{1}{2}}\left(\sin\omega\sum_{k=0}^{\infty}(-1)^{k}\frac{b_{2k}(% \nu)}{z^{2k}}+\cos\omega\sum_{k=0}^{\infty}(-1)^{k}\frac{b_{2k+1}(\nu)}{z^{2k+% 1}}\right),}}
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    DLMF:10.17.E9
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