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Symbolic evaluation of coefficients in Airy-type asymptotic expansions. (English) Zbl 1001.65024
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.
MSC:
65D20Computation of special functions, construction of tables
33C10Bessel and Airy functions, cylinder functions, 0 F 1
33F05Numerical approximation and evaluation of special functions
68W30Symbolic computation and algebraic computation
Software:
Maple