3 papers
math.CA2020
Elliptic umbilic representations connected with the caustic
E. G. Abramochkin, E. V. Razueva
We investigate the elliptic umbilic canonical integral with an approach based on a series expansion of its initial distribution shifted to the caustic points. An absolutely converg…
math.CA2017
Higher Derivatives of Airy Functions and of their Products
Eugeny G. Abramochkin, Evgeniya V. Razueva
The problem of evaluation of higher derivatives of Airy functions in a closed form is investigated. General expressions for the polynomials which have arisen in explicit formulae f…
math-ph2015
Mellin transform of quartic products of shifted Airy functions
E. G. Abramochkin, E. V. Razueva
The Mellin transform of quartic products of shifted Airy functions is evaluated in a closed form. Some particular cases expressed in terms of the logarithm function and complete el…