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Zbl 1001.65024
Vidunas, Raimundas; Temme, Nico M.
Symbolic evaluation of coefficients in Airy-type asymptotic expansions. (English)
[J] J. Math. Anal. Appl. 269, No.1, 317-331 (2002). ISSN 0022-247X

In constructing uniform asymptotic expansions of functions containing a large parameter it is sometimes used an integral representation of the same function. The authors consider the important case in which the integral representation yields uniform asymptotic expansions involving Airy functions and develop and discus computer algebra algorithms for evaluating the coefficients of such expansions. The coefficients are defined from recursive schemes obtained from integration by parts. The algorithms are illustrated with an application to Weber parabolic cylinder functions. The Maple code for this application is also given.
[Luigi Gatteschi (Torino)]

MSC 2000:: *65D20 Computation of special functions
33C10 Cylinder functions, etc.
33F05 Numerical approximation of special functions
68W30 Symbolic computation and algebraic computation

Keywords: Airy-type asymptotic expansions; symbolic computations; Maple algorithms; parabolic cylinder functions; Airy functions

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