Elementary Proofs of Algebraic Relationships for the Exponential and Logarithm Functions
File(s)
Date
1974Author
Epstein, H.I.
Caviness, B.F.
Publisher
University of Wisconsin-Madison Department of Computer Sciences
Metadata
Show full item recordAbstract
This paper uses elementary algebraic methods to obtain new proofs for theorems on algebraic relationships between the logarithmic and exponential functions. The main result is multivariate version of a special case of the Structure Theorem due to Risch that gives in a very explicit fashion the possible algebraic relationships between the exponential and logarithm functions. In addition there are some more results that give new information about the forms of elementary integrals of elementary functions as well as a new treatment of some algebraic dependence theorems previously discussed by Ostrowski, Kolchin and Ax.
Permanent Link
http://digital.library.wisc.edu/1793/57888Citation
TR223