DLMF:10.39.E6 (Q3574)

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DLMF:10.39.E6
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    Statements

    test
    K ν ⁡ ( z ) = π 1 2 ⁢ ( 2 ⁢ z ) ν ⁢ e - z ⁢ U ⁡ ( ν + 1 2 , 2 ⁢ ν + 1 , 2 ⁢ z ) , modified-Bessel-second-kind 𝜈 𝑧 superscript 𝜋 1 2 superscript 2 𝑧 𝜈 superscript 𝑒 𝑧 Kummer-confluent-hypergeometric-U 𝜈 1 2 2 𝜈 1 2 𝑧 {\displaystyle{\displaystyle K_{\nu}\left(z\right)=\pi^{\frac{1}{2}}(2z)^{\nu}% e^{-z}U\left(\nu+\tfrac{1}{2},2\nu+1,2z\right),}}
    0 references
    DLMF id
    DLMF:10.39.E6
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    Symbols used
    Kummer confluent hypergeometric function
    test
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2adec
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    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.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.m2acdec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1edec
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