DLMF:10.40.E8 (Q3586)

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DLMF:10.40.E8
No description defined

    Statements

    Defining formula
    ∂ ⁡ K ν ⁡ ( z ) ∂ ⁡ ν ∼ ( π 2 ⁢ z ) 1 2 ⁢ ν ⁢ e - z z ⁢ ∑ k = 0 ∞ α k ⁢ ( ν ) ( 8 ⁢ z ) k , asymptotic-expansion partial-derivative modified-Bessel-second-kind 𝜈 𝑧 𝜈 superscript 𝜋 2 𝑧 1 2 𝜈 superscript 𝑒 𝑧 𝑧 superscript subscript 𝑘 0 subscript 𝛼 𝑘 𝜈 superscript 8 𝑧 𝑘 {\displaystyle{\displaystyle\frac{\partial K_{\nu}\left(z\right)}{\partial\nu}% \sim\left(\frac{\pi}{2z}\right)^{\frac{1}{2}}\frac{\nu e^{-z}}{z}\sum_{k=0}^{% \infty}\frac{\alpha_{k}(\nu)}{(8z)^{k}},}}
    0 references
    DLMF id
    DLMF:10.40.E8
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    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11agdec
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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.m2aedec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
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    modified Bessel function of the second kind
    Defining formula
    K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E3.m2addec
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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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    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1edec
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    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1gdec
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    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1gdec
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