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DLMF:12.7.E8 - MaRDI portal

DLMF:12.7.E8 (Q4828)

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DLMF:12.7.E8
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    Statements

    DLMF defining formula
    U ⁡ ( - 2 , z ) = z 5 / 2 4 ⁢ 2 ⁢ π ⁢ ( 2 ⁢ K 1 4 ⁡ ( 1 4 ⁢ z 2 ) + 3 ⁢ K 3 4 ⁡ ( 1 4 ⁢ z 2 ) - K 5 4 ⁡ ( 1 4 ⁢ z 2 ) ) , parabolic-U 2 𝑧 superscript 𝑧 5 2 4 2 𝜋 2 modified-Bessel-second-kind 1 4 1 4 superscript 𝑧 2 3 modified-Bessel-second-kind 3 4 1 4 superscript 𝑧 2 modified-Bessel-second-kind 5 4 1 4 superscript 𝑧 2 {\displaystyle{\displaystyle U\left(-2,z\right)=\frac{z^{5/2}}{4\sqrt{2\pi}}% \left(2K_{\frac{1}{4}}\left(\tfrac{1}{4}z^{2}\right)+3K_{\frac{3}{4}}\left(% \tfrac{1}{4}z^{2}\right)-K_{\frac{5}{4}}\left(\tfrac{1}{4}z^{2}\right)\right),}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    modified Bessel function of the second kind
    DLMF 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
    0 references
    Q11291
    DLMF defining formula
    U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C12.S2.SS1.p1.m1aedec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C12.S1.XMD3.m1gdec
    0 references

    Identifiers

     
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