DLMF:11.10.E27 (Q4049)

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DLMF:11.10.E27
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    Statements

    Defining formula
    ∂ ∂ ⁡ ν ⁡ 𝐉 ν ⁡ ( z ) | ν = 0 = 1 2 ⁢ π ⁢ 𝐇 0 ⁡ ( z ) , evaluated-at partial-derivative 𝜈 Anger-J 𝜈 𝑧 𝜈 0 1 2 𝜋 Struve-H 0 𝑧 {\displaystyle{\displaystyle\left.\frac{\partial}{\partial\nu}\mathbf{J}_{\nu}% \left(z\right)\right|_{\nu=0}=\tfrac{1}{2}\pi\mathbf{H}_{0}\left(z\right),}}
    0 references
    DLMF id
    DLMF:11.10.E27
    0 references
    Symbols used
    Anger function
    Defining formula
    𝐉 ν ⁡ ( z ) Anger-J 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{J}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E1.m2andec
    0 references
    Struve function
    Defining formula
    𝐇 ν ⁡ ( z ) Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E1.m2acdec
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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.m2audec
    0 references
    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.m4adec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2adec
    0 references
    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1xdec
    0 references
     
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