Extensions of Asymptotic Fields Via Meromorphic Functions |
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Authors: | Shackell John |
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Institution: | University of Kent at Canterbury Canterbury, Kent CT2 7NF |
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Abstract: | An asymptotic field is a special type of Hardy field in which,modulo an oracle for constants, one can determine asymptoticbehaviour of elements. In a previous paper, it was shown inparticular that limits of real Liouvillian functions can therebybe computed. Let denote an asymptotic field and let f . Weprove here that if G is meromorphic at the limit of f (whichmay be infinite) and satisfies an algebraic differential equationover R(x), then (G o f) is an asymptotic field. Hence it ispossible (modulo an oracle for constants) to compute asymptoticforms for elements of (G o f). An example is given to show thatthe result may fail if G has an essential singularity at limf. |
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