DLMF:10.39.E2 (Q3570)

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DLMF:10.39.E2
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    Statements

    Defining formula
    K 1 2 ⁡ ( z ) = K - 1 2 ⁡ ( z ) = ( π 2 ⁢ z ) 1 2 ⁢ e - z . modified-Bessel-second-kind 1 2 𝑧 modified-Bessel-second-kind 1 2 𝑧 superscript 𝜋 2 𝑧 1 2 superscript 𝑒 𝑧 {\displaystyle{\displaystyle K_{\frac{1}{2}}\left(z\right)=K_{-\frac{1}{2}}% \left(z\right)=\left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}.}}
    0 references
    DLMF id
    DLMF:10.39.E2
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    modified Bessel function of the second kind
    Defining formula
    K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E3.m2adec
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    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1adec
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