DLMF:10.34.E5 (Q3546)

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DLMF:10.34.E5
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    Statements

    test
    K n ⁡ ( z ⁢ e m ⁢ π ⁢ i ) = ( - 1 ) m ⁢ n ⁢ K n ⁡ ( z ) + ( - 1 ) n ⁢ ( m - 1 ) - 1 ⁢ m ⁢ π ⁢ i ⁢ I n ⁡ ( z ) , modified-Bessel-second-kind 𝑛 𝑧 superscript 𝑒 𝑚 𝜋 𝑖 superscript 1 𝑚 𝑛 modified-Bessel-second-kind 𝑛 𝑧 superscript 1 𝑛 𝑚 1 1 𝑚 𝜋 𝑖 modified-Bessel-first-kind 𝑛 𝑧 {\displaystyle{\displaystyle K_{n}\left(ze^{m\pi i}\right)=(-1)^{mn}K_{n}\left% (z\right)+(-1)^{n(m-1)-1}m\pi iI_{n}\left(z\right),}}
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    DLMF id
    DLMF:10.34.E5
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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.m2addec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
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