Elliptic umbilic representations connected with the caustic

E G Abramochkin and E V Razueva
Lebedev Physical Institute, Samara, 443011, Russia

We investigate the elliptic umbilic canonical integral, well known in catastrophe theory and optics, with an approach based on a series expansion of its initial distribution shifted to the caustic points. An absolutely convergent integral representation for the elliptic umbilic in terms of Airy functions is obtained. It provides an approach for numerical evaluation of the elliptic umbilic. In particular, it helps to find out new relations between the elliptic umbilic and 2F2 hypergeometric function. © Anita Publications. All rights reserved.
Keywords: Diffraction catastrophes, Caustics, Airy functions, Hypergeometric function.

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