DLMF:36.2.E29 (Q9871)

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DLMF:36.2.E29
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    Statements

    Defining formula
    Ψ ( H ) ⁡ ( 0 , 0 , z ) = Ψ ( H ) ⁡ ( 0 , 0 , - z ) ¯ = 2 1 / 3 3 ⁢ exp ⁡ ( 1 27 ⁢ i ⁢ z 3 ) ⁢ Ψ ( E ) ⁡ ( 0 , 0 , - z 2 2 / 3 ) , hyperbolic-umbilic-canonical-integral 0 0 𝑧 hyperbolic-umbilic-canonical-integral 0 0 𝑧 superscript 2 1 3 3 1 27 𝑖 superscript 𝑧 3 elliptic-umbilic-canonical-integral 0 0 𝑧 superscript 2 2 3 {\displaystyle{\displaystyle\Psi^{(\mathrm{H})}\left(0,0,z\right)=\overline{% \Psi^{(\mathrm{H})}\left(0,0,-z\right)}=\frac{2^{1/3}}{\sqrt{3}}\exp\left(% \frac{1}{27}iz^{3}\right)\Psi^{(\mathrm{E})}\left(0,0,-\frac{z}{2^{2/3}}\right% ),}}
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    DLMF id
    DLMF:36.2.E29
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    constraint
    - ∞ < z < ∞ 𝑧 {\displaystyle{\displaystyle-\infty<z<\infty}}
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    Symbols used
    complex conjugate
    Defining formula
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2acdec
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