DLMF:36.2.E20 (Q9862)

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DLMF:36.2.E20
No description defined

    Statements

    Defining formula
    Ψ ( E ) ⁡ ( x , y , 0 ) = 2 ⁢ π 2 ⁢ ( 2 3 ) 2 / 3 ⁢ ℜ ⁡ ( Ai ⁡ ( x + i ⁢ y 12 1 / 3 ) ⁢ Bi ⁡ ( x - i ⁢ y 12 1 / 3 ) ) , elliptic-umbilic-canonical-integral 𝑥 𝑦 0 2 superscript 𝜋 2 superscript 2 3 2 3 Airy-Ai 𝑥 𝑖 𝑦 superscript 12 1 3 Airy-Bi 𝑥 𝑖 𝑦 superscript 12 1 3 {\displaystyle{\displaystyle\Psi^{(\mathrm{E})}\left(x,y,0\right)=2\pi^{2}(% \tfrac{2}{3})^{2/3}\Re\left(\mathrm{Ai}\left(\frac{x+iy}{12^{1/3}}\right)% \mathrm{Bi}\left(\frac{x-iy}{12^{1/3}}\right)\right),}}
    0 references
    DLMF id
    DLMF:36.2.E20
    0 references
    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1acdec
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    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2adec
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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.m2ajdec
    0 references
    elliptic umbilic canonical integral function
    Defining formula
    Ψ ( E ) ⁡ ( 𝐱 ) elliptic-umbilic-canonical-integral 𝐱 {\displaystyle{\displaystyle\Psi^{(\mathrm{E})}\left(\NVar{\mathbf{x}}\right)}}
    xml-id
    C36.S2.E5.m3addec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2andec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
    Q12745
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C36.S1.XMD10.m1gdec
    0 references
    Q12748
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C36.S1.XMD9.m1gdec
    0 references
     
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