Extensions of Asymptotic Fields via Meromorphic Functions
نویسنده
چکیده
An asymptotic field is a special type of Hardy field in which, modulo an oracle for constants, one can determine asymptotic behaviour of elements. In a previous paper, it was shown in particular that limits of real Liouvillian functions can thereby be computed. Let !F denote an asymptotic field and l e t / e^" . We prove here that if G is meromorphic at the limit of/(which may be infinite) and satisfies an algebraic differential equation over IR(.v), then 3?(Gof) is an asymptotic field. Hence it is possible (modulo an oracle for constants) to compute asymptotic forms for elements of F ( (?o / ) . An example is given to show that the result may fail if G has an essential singularity at lim/.
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