Computer algebra algorithms are developed for evaluating the coefficientsin Airy-type asymptotic expansions that are obtained fromintegrals with a large parameter. The coefficients are defined from recursiveschemes obtained from integration by parts. An application is given forthe Weber parabolic cylinder function.

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (msc 41A60), Bessel and Airy functions, cylinder functions, ${}_0F_1$ (msc 33C10), Confluent hypergeometric functions, Whittaker functions, ${}_1F_1$ (msc 33C15), Numerical approximation and evaluation (msc 33F05), Computation of special functions, construction of tables (msc 65D20)
Modelling, Analysis and Simulation [MAS]
Computational Dynamics

Vidunas, R, & Temme, N.M. (2001). Symbolic evaluation of coefficients in Airy-type asymptotic expansions. Modelling, Analysis and Simulation [MAS]. CWI.