DLMF:10.15.E9 (Q3155)

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DLMF:10.15.E9
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    Statements

    Defining formula
    ∂ ⁡ Y ν ⁡ ( x ) ∂ ⁡ ν | ν = - 1 2 = - 2 π ⁢ x ⁢ ( Ci ⁡ ( 2 ⁢ x ) ⁢ sin ⁡ x - ( Si ⁡ ( 2 ⁢ x ) - π ) ⁢ cos ⁡ x ) . evaluated-at partial-derivative Bessel-Y-Weber 𝜈 𝑥 𝜈 𝜈 1 2 2 𝜋 𝑥 cosine-integral 2 𝑥 𝑥 sine-integral 2 𝑥 𝜋 𝑥 {\displaystyle{\displaystyle\left.\frac{\partial Y_{\nu}\left(x\right)}{% \partial\nu}\right|_{\nu=-\frac{1}{2}}=-\sqrt{\frac{2}{\pi x}}\left(\mathrm{Ci% }\left(2x\right)\sin x-\left(\mathrm{Si}\left(2x\right)-\pi\right)\cos x\right% ).}}
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    DLMF id
    DLMF:10.15.E9
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    Symbols used
    Bessel function of the second kind
    Defining formula
    Y ν ⁡ ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E3.m2aedec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2acdec
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    cosine integral
    Defining formula
    Ci ⁡ ( z ) cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E11.m2acdec
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    partial derivative of $$f$$ with respect to $$x$$
    Defining formula
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4ahdec
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    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2ahdec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2acdec
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    sine integral
    Defining formula
    Si ⁡ ( z ) sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E9.m2acdec
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    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1cdec
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