DLMF:10.34.E2 (Q3543)

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DLMF:10.34.E2
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    Statements

    test
    K ν ⁡ ( z ⁢ e m ⁢ π ⁢ i ) = e - m ⁢ ν ⁢ π ⁢ i ⁢ K ν ⁡ ( z ) - π ⁢ i ⁢ sin ⁡ ( m ⁢ ν ⁢ π ) ⁢ csc ⁡ ( ν ⁢ π ) ⁢ I ν ⁡ ( z ) . modified-Bessel-second-kind 𝜈 𝑧 superscript 𝑒 𝑚 𝜋 𝑖 superscript 𝑒 𝑚 𝜈 𝜋 𝑖 modified-Bessel-second-kind 𝜈 𝑧 𝜋 𝑖 𝑚 𝜈 𝜋 𝜈 𝜋 modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\nu}\left(ze^{m\pi i}\right)=e^{-m\nu\pi i}K_{% \nu}\left(z\right)-\pi i\sin\left(m\nu\pi\right)\csc\left(\nu\pi\right)I_{\nu}% \left(z\right).}}
    0 references
    DLMF id
    DLMF:10.34.E2
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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.m2aadec
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    cosecant function
    test
    csc ⁡ z 𝑧 {\displaystyle{\displaystyle\csc\NVar{z}}}
    xml-id
    C4.S14.E5.m2adec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
     
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