DLMF:10.15.E2 (Q3148)

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DLMF:10.15.E2
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    Statements

    Defining formula
    ∂ ⁡ Y ν ⁡ ( z ) ∂ ⁡ ν = cot ⁡ ( ν ⁢ π ) ⁢ ( ∂ ⁡ J ν ⁡ ( z ) ∂ ⁡ ν - π ⁢ Y ν ⁡ ( z ) ) - csc ⁡ ( ν ⁢ π ) ⁢ ∂ ⁡ J - ν ⁡ ( z ) ∂ ⁡ ν - π ⁢ J ν ⁡ ( z ) . partial-derivative Bessel-Y-Weber 𝜈 𝑧 𝜈 𝜈 𝜋 partial-derivative Bessel-J 𝜈 𝑧 𝜈 𝜋 Bessel-Y-Weber 𝜈 𝑧 𝜈 𝜋 partial-derivative Bessel-J 𝜈 𝑧 𝜈 𝜋 Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle\frac{\partial Y_{\nu}\left(z\right)}{\partial\nu}% =\cot\left(\nu\pi\right)\left(\frac{\partial J_{\nu}\left(z\right)}{\partial% \nu}-\pi Y_{\nu}\left(z\right)\right)-\csc\left(\nu\pi\right)\frac{\partial J_% {-\nu}\left(z\right)}{\partial\nu}-\pi J_{\nu}\left(z\right).}}
    0 references
    DLMF id
    DLMF:10.15.E2
    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.m2aadec
    0 references
    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.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    cosecant function
    Defining formula
    csc ⁡ z 𝑧 {\displaystyle{\displaystyle\csc\NVar{z}}}
    xml-id
    C4.S14.E5.m2adec
    0 references
    cotangent function
    Defining formula
    cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}
    xml-id
    C4.S14.E7.m2adec
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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.m4aadec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2aadec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1adec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1adec
    0 references
     
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