DLMF:10.47.E9 (Q3677)

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DLMF:10.47.E9
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    Statements

    test
    𝗄 n ⁡ ( z ) = 1 2 ⁢ π / z ⁢ K n + 1 2 ⁡ ( z ) = 1 2 ⁢ π / z ⁢ K - n - 1 2 ⁡ ( z ) . spherical-Bessel-K 𝑛 𝑧 1 2 𝜋 𝑧 modified-Bessel-second-kind 𝑛 1 2 𝑧 1 2 𝜋 𝑧 modified-Bessel-second-kind 𝑛 1 2 𝑧 {\displaystyle{\displaystyle\mathsf{k}_{n}\left(z\right)=\sqrt{\tfrac{1}{2}\pi% /z}K_{n+\frac{1}{2}}\left(z\right)=\sqrt{\tfrac{1}{2}\pi/z}K_{-n-\frac{1}{2}}% \left(z\right).}}
    0 references
    DLMF id
    DLMF:10.47.E9
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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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    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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