DLMF:12.7.E11 (Q4134)

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DLMF:12.7.E11
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    Statements

    Defining formula
    U ⁡ ( 1 , z ) = z 3 / 2 2 ⁢ π ⁢ ( K 3 4 ⁡ ( 1 4 ⁢ z 2 ) - K 1 4 ⁡ ( 1 4 ⁢ z 2 ) ) . parabolic-U 1 𝑧 superscript 𝑧 3 2 2 𝜋 modified-Bessel-second-kind 3 4 1 4 superscript 𝑧 2 modified-Bessel-second-kind 1 4 1 4 superscript 𝑧 2 {\displaystyle{\displaystyle U\left(1,z\right)=\frac{z^{3/2}}{\sqrt{2\pi}}% \left(K_{\frac{3}{4}}\left(\tfrac{1}{4}z^{2}\right)-K_{\frac{1}{4}}\left(% \tfrac{1}{4}z^{2}\right)\right).}}
    0 references
    DLMF id
    DLMF:12.7.E11
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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.m2ahdec
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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.m2acdec
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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.m1ahdec
    0 references
     
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