DLMF:10.40.E10 (Q3588)

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DLMF:10.40.E10
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    Statements

    test
    K ν ⁡ ( z ) = ( π 2 ⁢ z ) 1 2 ⁢ e - z ⁢ ( ∑ k = 0 ℓ - 1 a k ⁢ ( ν ) z k + R ℓ ⁢ ( ν , z ) ) , modified-Bessel-second-kind 𝜈 𝑧 superscript 𝜋 2 𝑧 1 2 superscript 𝑒 𝑧 superscript subscript 𝑘 0 ℓ 1 subscript 𝑎 𝑘 𝜈 superscript 𝑧 𝑘 subscript 𝑅 ℓ 𝜈 𝑧 {\displaystyle{\displaystyle K_{\nu}\left(z\right)=\left(\frac{\pi}{2z}\right)% ^{\frac{1}{2}}e^{-z}\left(\sum_{k=0}^{\ell-1}\frac{a_{k}(\nu)}{z^{k}}+R_{\ell}% (\nu,z)\right),}}
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    DLMF id
    DLMF:10.40.E10
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    constraint
    ℓ = 1 , 2 , … ℓ 1 2 … {\displaystyle{\displaystyle\ell=1,2,\ldots}}
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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.m2afdec
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