Parabolic Cylinder Functions: Examples of Error Bounds For Asymptotic Expansions. Modelling, Analysis and Simulation. (MAS)

摘要

Several asymptotic expansions of parabolic cylinder functions are discussed and error bounds for remainders in the expansions are presented. In particular Poincare-type expansions for large values of the arguments z and uniform expanisons for large values of the parameter are considered. It is shown how expanions can be derived by using the differential equation, and, for a special case, how an integral representation can be used. The expansions are based on those given in Olver (1959) and on modifications of these expansions given in Temme (200). Computer algebra techniques are used for obtaining representations of the bounds and for numerical computations.