Extensions of Asymptotic Fields Via Meromorphic Functions | Zendy

Shackell John | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

Extensions of Asymptotic Fields Via Meromorphic Functions

Author(s) -

Shackell John

Publication year - 1995

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/jlms/52.2.356

Subject(s) - meromorphic function , mathematics , modulo , limit (mathematics) , field (mathematics) , algebraic number , constant (computer programming) , asymptotic analysis , singularity , asymptotic formula , pure mathematics , type (biology) , mathematical analysis , discrete mathematics , computer science , programming language , ecology , biology

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 let f ∈ 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 ( G o f ) is an asymptotic field. Hence it is possible (modulo an oracle for constants) to compute asymptotic forms for elements of ℱ( G o f ). An example is given to show that the result may fail if G has an essential singularity at lim f .

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research