DLMF:10.27.E4 (Q3494)

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DLMF:10.27.E4
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    Statements

    test
    K ν ⁡ ( z ) = 1 2 ⁢ π ⁢ I - ν ⁡ ( z ) - I ν ⁡ ( z ) sin ⁡ ( ν ⁢ π ) . modified-Bessel-second-kind 𝜈 𝑧 1 2 𝜋 modified-Bessel-first-kind 𝜈 𝑧 modified-Bessel-first-kind 𝜈 𝑧 𝜈 𝜋 {\displaystyle{\displaystyle K_{\nu}\left(z\right)=\tfrac{1}{2}\pi\frac{I_{-% \nu}\left(z\right)-I_{\nu}\left(z\right)}{\sin\left(\nu\pi\right)}.}}
    0 references
    DLMF id
    DLMF:10.27.E4
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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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    modified Bessel function of the first kind
    test
    I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E2.m2abdec
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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.m2abdec
    0 references
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
     
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