Polynomials Associated with the Higher Derivatives of the Airy Functions Ai(z) and Ai'(z)

The Airy function Ai(z) and its derivative Ai'(z) occur in a large number of applications in Chemistry and Physics. As a result, there is a continuing interest in the properties of these functions. Recently, there has been interest in obtaining general expressions for the higher derivatives of these functions. In this work, general expressions for the polynomials which are contained in these derivatives are given in terms of the partial Bell polynomials.