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We investigate the elliptic umbilic canonical integral with an approach basedon a series expansion of its initial distribution shifted to the causticpoints. An absolutely convergent integral representation for the ellipticumbilic is obtained. Using it, we find the elliptic umbilic particular valuesin terms of 2F2 hypergeometric functions. We also derive an integral over theproduct of Gaussian and two Airy functions in terms of Bessel functions offractional orders. Some other corollaries including 3F2 hypergeometric functionspecial values and the Airy polynomials relations are also discussed.

Elliptic umbilic representations connected with the caustic