DLMF:10.15.E6 (Q3152)

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DLMF:10.15.E6
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    Defining formula
    ∂ ⁡ J ν ⁡ ( x ) ∂ ⁡ ν | ν = 1 2 = 2 π ⁢ x ⁢ ( Ci ⁡ ( 2 ⁢ x ) ⁢ sin ⁡ x - Si ⁡ ( 2 ⁢ x ) ⁢ cos ⁡ x ) , evaluated-at partial-derivative Bessel-J 𝜈 𝑥 𝜈 𝜈 1 2 2 𝜋 𝑥 cosine-integral 2 𝑥 𝑥 sine-integral 2 𝑥 𝑥 {\displaystyle{\displaystyle\left.\frac{\partial J_{\nu}\left(x\right)}{% \partial\nu}\right|_{\nu=\frac{1}{2}}=\sqrt{\frac{2}{\pi x}}\left(\mathrm{Ci}% \left(2x\right)\sin x-\mathrm{Si}\left(2x\right)\cos x\right),}}
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    DLMF id
    DLMF:10.15.E6
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