DLMF:10.38.E2 (Q3561)

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DLMF:10.38.E2
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    Statements

    test
    ∂ ⁡ K ν ⁡ ( z ) ∂ ⁡ ν = 1 2 ⁢ π ⁢ csc ⁡ ( ν ⁢ π ) ⁢ ( ∂ ⁡ I - ν ⁡ ( z ) ∂ ⁡ ν - ∂ ⁡ I ν ⁡ ( z ) ∂ ⁡ ν ) - π ⁢ cot ⁡ ( ν ⁢ π ) ⁢ K ν ⁡ ( z ) , partial-derivative modified-Bessel-second-kind 𝜈 𝑧 𝜈 1 2 𝜋 𝜈 𝜋 partial-derivative modified-Bessel-first-kind 𝜈 𝑧 𝜈 partial-derivative modified-Bessel-first-kind 𝜈 𝑧 𝜈 𝜋 𝜈 𝜋 modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle\frac{\partial K_{\nu}\left(z\right)}{\partial\nu}% =\tfrac{1}{2}\pi\csc\left(\nu\pi\right)\*\left(\frac{\partial I_{-\nu}\left(z% \right)}{\partial\nu}-\frac{\partial I_{\nu}\left(z\right)}{\partial\nu}\right% )-\pi\cot\left(\nu\pi\right)K_{\nu}\left(z\right),}}
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    DLMF id
    DLMF:10.38.E2
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    constraint
    ν ∉ ℤ 𝜈 {\displaystyle{\displaystyle\nu\notin\mathbb{Z}}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    cosecant function
    test
    csc ⁡ z 𝑧 {\displaystyle{\displaystyle\csc\NVar{z}}}
    xml-id
    C4.S14.E5.m2adec
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    cotangent function
    test
    cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}
    xml-id
    C4.S14.E7.m2adec
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    Q10818
    test
    ℤ {\displaystyle{\displaystyle\mathbb{Z}}}
    xml-id
    introduction.Sx4.p2.t1.r20.m2adec
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    modified Bessel function of the first kind
    test
    I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E2.m2aadec
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    modified Bessel function of the second kind
    test
    K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E3.m2adec
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    Q11245
    test
    ∉ {\displaystyle{\displaystyle\notin}}
    xml-id
    introduction.Sx4.p1.t1.r11.m2adec
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