DLMF:10.39.E4 (Q3572)

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DLMF:10.39.E4
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    Statements

    test
    K 3 4 ⁡ ( z ) = 1 2 ⁢ π 1 2 ⁢ z - 3 4 ⁢ ( 1 2 ⁢ U ⁡ ( 1 , 2 ⁢ z 1 2 ) + U ⁡ ( - 1 , 2 ⁢ z 1 2 ) ) . modified-Bessel-second-kind 3 4 𝑧 1 2 superscript 𝜋 1 2 superscript 𝑧 3 4 1 2 parabolic-U 1 2 superscript 𝑧 1 2 parabolic-U 1 2 superscript 𝑧 1 2 {\displaystyle{\displaystyle K_{\frac{3}{4}}\left(z\right)=\tfrac{1}{2}\pi^{% \frac{1}{2}}z^{-\frac{3}{4}}\left(\tfrac{1}{2}U\left(1,2z^{\frac{1}{2}}\right)% +U\left(-1,2z^{\frac{1}{2}}\right)\right).}}
    0 references
    DLMF id
    DLMF:10.39.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.m2acdec
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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
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    Q11320
    test
    U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C12.S2.SS1.p1.m1aadec
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