DLMF:12.2.E12 (Q4097)

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DLMF:12.2.E12
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    Statements

    Defining formula
    𝒲 ⁡ { U ⁡ ( a , z ) , U ⁡ ( - a , ± i ⁢ z ) } = ∓ i ⁢ e ± i ⁢ π ⁢ ( 1 2 ⁢ a + 1 4 ) . Wronskian parabolic-U 𝑎 𝑧 parabolic-U 𝑎 plus-or-minus 𝑖 𝑧 minus-or-plus 𝑖 superscript 𝑒 plus-or-minus 𝑖 𝜋 1 2 𝑎 1 4 {\displaystyle{\displaystyle\mathscr{W}\left\{U\left(a,z\right),U\left(-a,\pm iz% \right)\right\}=\mp ie^{\pm i\pi(\frac{1}{2}a+\frac{1}{4})}.}}
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    DLMF id
    DLMF:12.2.E12
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    Symbols used
    Q10865
    Defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3abdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
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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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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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