Symbolic Asymptotics: Functions of Two Variables, Implicit Functions

✍ Scribed by B. Salvy; J. Shackell

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 564 KB
• Volume: 25
• Category: Article
• ISSN: 0747-7171
• DOI: 10.1006/jsco.1997.0179

✦ Synopsis

A number of recent papers have been concerned with algorithms to decide the limiting behaviour of functions of a single variable. Here we make a corresponding study of a class of functions of two variables, namely the exp-log functions. As in the one-variable case, we need to make certain assumptions regarding the handling of constants.

Two of the main tools in the one-variable case are Hardy fields and nested forms. Here, we show how to compute some asymptotic estimates for two-variable exp-log functions. This method is then used to give an algorithm for computing the nested forms of real implicit functions.