DLMF:10.39.E3 (Q3571)

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DLMF:10.39.E3
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    Statements

    Defining formula
    K 1 4 ⁡ ( z ) = π 1 2 ⁢ z - 1 4 ⁢ U ⁡ ( 0 , 2 ⁢ z 1 2 ) , modified-Bessel-second-kind 1 4 𝑧 superscript 𝜋 1 2 superscript 𝑧 1 4 parabolic-U 0 2 superscript 𝑧 1 2 {\displaystyle{\displaystyle K_{\frac{1}{4}}\left(z\right)=\pi^{\frac{1}{2}}z^% {-\frac{1}{4}}U\left(0,2z^{\frac{1}{2}}\right),}}
    0 references
    DLMF id
    DLMF:10.39.E3
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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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.m2aadec
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    Q11320
    Defining formula
    U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C12.S2.SS1.p1.m1adec
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    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1bdec
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