DLMF:10.15.E7 (Q3153)

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DLMF:10.15.E7
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    Statements

    Defining formula
    ∂ ⁡ J ν ⁡ ( x ) ∂ ⁡ ν | ν = - 1 2 = 2 π ⁢ x ⁢ ( Ci ⁡ ( 2 ⁢ x ) ⁢ cos ⁡ x + Si ⁡ ( 2 ⁢ x ) ⁢ sin ⁡ 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)\cos x+\mathrm{Si}\left(2x\right)\sin x\right),}}
    0 references
    DLMF id
    DLMF:10.15.E7
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2afdec
    0 references
     
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