Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 042, 26 pages      arXiv:1707.05218      https://doi.org/10.3842/SIGMA.2018.042

Higher Derivatives of Airy Functions and of their Products

Eugeny G. Abramochkin and Evgeniya V. Razueva
Coherent Optics Lab, Lebedev Physical Institute, Samara, 443011, Russia

Received October 13, 2017, in final form April 26, 2018; Published online May 05, 2018

Abstract
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 for these derivatives are given in terms of particular values of Gegenbauer polynomials. Similar problem for products of Airy functions is solved in terms of terminating hypergeometric series.

Key words: Airy functions; Gegenbauer polynomials; hypergeometric function.

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