DLMF:10.39.E8 (Q3576)

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DLMF:10.39.E8
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    Statements

    test
    K ν ⁡ ( z ) = ( π 2 ⁢ z ) 1 2 ⁢ W 0 , ν ⁡ ( 2 ⁢ z ) . modified-Bessel-second-kind 𝜈 𝑧 superscript 𝜋 2 𝑧 1 2 Whittaker-confluent-hypergeometric-W 0 𝜈 2 𝑧 {\displaystyle{\displaystyle K_{\nu}\left(z\right)=\left(\frac{\pi}{2z}\right)% ^{\frac{1}{2}}W_{0,\nu}\left(2z\right).}}
    0 references
    DLMF id
    DLMF:10.39.E8
    0 references
    Symbols used
    Whittaker confluent hypergeometric function
    test
    W κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E3.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    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.m2addec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1gdec
    0 references
    Q11427
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1cdec
    0 references
     
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