DLMF:36.2.E21 (Q9863)

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DLMF:36.2.E21
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    Statements

    Defining formula
    Ψ ( H ) ⁡ ( x , y , 0 ) = 4 ⁢ π 2 3 2 / 3 ⁢ Ai ⁡ ( x 3 1 / 3 ) ⁢ Ai ⁡ ( y 3 1 / 3 ) . hyperbolic-umbilic-canonical-integral 𝑥 𝑦 0 4 superscript 𝜋 2 superscript 3 2 3 Airy-Ai 𝑥 superscript 3 1 3 Airy-Ai 𝑦 superscript 3 1 3 {\displaystyle{\displaystyle\Psi^{(\mathrm{H})}\left(x,y,0\right)=\frac{4\pi^{% 2}}{3^{2/3}}\mathrm{Ai}\left(\frac{x}{3^{1/3}}\right)\mathrm{Ai}\left(\frac{y}% {3^{1/3}}\right).}}
    0 references
    DLMF id
    DLMF:36.2.E21
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    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1addec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2akdec
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    hyperbolic umbilic canonical integral function
    Defining formula
    Ψ ( H ) ⁡ ( 𝐱 ) hyperbolic-umbilic-canonical-integral 𝐱 {\displaystyle{\displaystyle\Psi^{(\mathrm{H})}\left(\NVar{\mathbf{x}}\right)}}
    xml-id
    C36.S2.E5.m4addec
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