General algorithms in asymptotics I: Gonnet and Gruntz' algorithm


General algorithms in asymptotics are used to obtain automatically asymptotic information about explicit functions, or solutions to certain types of equations. The simplest non trivial problem is the automatic expansion of exp-log functions. Shackell was the first to give an algorithm and Gonnet and Gruntz were the first to implement one. We will clarify the latter one and put it into a theoretical context. Our study serves as a base for generalisations to more general classes of functions.

Keywords: asymptotic expansion, exp-log function, transseries, algorithm

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