Shackell, J. (1995) Extensions of asymptotic fields via meromorphic functions. Journal of the London Mathematical Society-Second Series, 52 (part 2). pp. 356-374. ISSN 0024-6107. (The full text of this publication is not available from this repository)
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An asymptotic field is a special type of Hardy field in which, module 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 let f is an element of F. We prove here that if G is meromorphic at the limit of f (which may be infinite) and satisfies an algebraic differential equation over R(x), then F(Gof) is an asymptotic field. Hence it is possible (module an oracle for constants) to compute asymptotic forms for elements of F(Gof). An example is given to show that the result may fail if G has an essential singularity at limf.
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science|
|Depositing User:||I.T. Ekpo|
|Date Deposited:||31 Oct 2009 15:43|
|Last Modified:||31 Oct 2009 15:43|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/19037 (The current URI for this page, for reference purposes)|