Complex Variables 28:27-36 (1995)

© 1995 OPA (Overseas Publishers Association) Amsterdam B.V.

AMS 1991: 34A20

Abstract: Differential fields of germs of continuous real valued functions of one real variable (Hardy fields) have the property that all elements have limits in the extended real numbers and thus have a canonical valuation. For differential fields of holomorphic germs this is not generally the case. We provide a criterion for differential fields of holomorphic germs for its elements to have uniform limits in a partial neighborhood of infinity as an extended complex number. We apply the criterion to the specific case of a differential field of germs generated by the solutions of the Riccati equation W'+W ²= e ^2z and extend the asymptotic validity of the usual series for the solutions from the positive real axis to a region in the complex plane.

@article{dg:lim,author={Gokhman, D.},
title={Limits in differential fields of complex germs},
journal={Complex Variables},volume={28},pages={27--36},year={1995}}