DLMF:10.34.E6 (Q3547)

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DLMF:10.34.E6
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    Statements

    test
    K n ⁡ ( z ⁢ e m ⁢ π ⁢ i ) = ± ( - 1 ) n ⁢ ( m - 1 ) ⁢ m ⁢ K n ⁡ ( z ⁢ e ± π ⁢ i ) ∓ ( - 1 ) n ⁢ m ⁢ ( m ∓ 1 ) ⁢ K n ⁡ ( z ) . modified-Bessel-second-kind 𝑛 𝑧 superscript 𝑒 𝑚 𝜋 𝑖 minus-or-plus plus-or-minus superscript 1 𝑛 𝑚 1 𝑚 modified-Bessel-second-kind 𝑛 𝑧 superscript 𝑒 plus-or-minus 𝜋 𝑖 superscript 1 𝑛 𝑚 minus-or-plus 𝑚 1 modified-Bessel-second-kind 𝑛 𝑧 {\displaystyle{\displaystyle K_{n}\left(ze^{m\pi i}\right)=\pm(-1)^{n(m-1)}mK_% {n}\left(ze^{\pm\pi i}\right)\mp(-1)^{nm}(m\mp 1)K_{n}\left(z\right).}}
    0 references
    DLMF id
    DLMF:10.34.E6
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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.m2aedec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
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