Formula:10653

Digital Library of Mathematical Functions ID 36.9.E8

${\displaystyle{\displaystyle\left|\Psi^{(\mathrm{H})}\left(x,y,z\right)\right|^{2}=8\pi^{2}\left(\frac{2}{9}\right)^{1/3}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\mathrm{Ai}\left(\left(\frac{4}{3}\right)^{1/3}(x+zv+3u^{2})\right)\mathrm{Ai}\left(\left(\frac{4}{3}\right)^{1/3}(y+zu+3v^{2})\right)\mathrm{d}u\mathrm{d}v.}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\Psi^{(\mathrm{H})}\left(\NVar{\mathbf{x}}\right)}}$: hyperbolic umbilic canonical integral function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle y}}$: real parameter
• ${\displaystyle{\displaystyle z}}$: real parameter
• ${\displaystyle{\displaystyle x}}$: real parameter
 

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