DLMF:10.2.E4 (Q3008)

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DLMF:10.2.E4
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    Statements

    Defining formula
    Y n ⁡ ( z ) = 1 π ⁢ ∂ ⁡ J ν ⁡ ( z ) ∂ ⁡ ν | ν = n + ( - 1 ) n π ⁢ ∂ ⁡ J ν ⁡ ( z ) ∂ ⁡ ν | ν = - n , Bessel-Y-Weber 𝑛 𝑧 evaluated-at 1 𝜋 partial-derivative Bessel-J 𝜈 𝑧 𝜈 𝜈 𝑛 evaluated-at superscript 1 𝑛 𝜋 partial-derivative Bessel-J 𝜈 𝑧 𝜈 𝜈 𝑛 {\displaystyle{\displaystyle Y_{n}\left(z\right)=\frac{1}{\pi}\left.\frac{% \partial J_{\nu}\left(z\right)}{\partial\nu}\right|_{\nu=n}+\left.\frac{(-1)^{% n}}{\pi}\frac{\partial J_{\nu}\left(z\right)}{\partial\nu}\right|_{\nu=-n},}}
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    DLMF id
    DLMF:10.2.E4
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    constraint
    n = 0 , ± 1 , ± 2 , … 𝑛 0 plus-or-minus 1 plus-or-minus 2 … {\displaystyle{\displaystyle n=0,\pm 1,\pm 2,\ldots}}
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    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.m2abdec
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    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.m2aadec
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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.m2aadec
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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.m4adec
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    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2adec
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