Article contents
A Class of functional equations which have entire solutions
Published online by Cambridge University Press: 17 April 2009
Abstract
We consider the Abelian functional equation
where φ is a given entire function and g is to be found. The inverse function f = g−1 (if one exists) must satisfy
We show that for a wide class of entire functions, which includes φ(z) = ez − 1, the latter equation has a non-constant entire solution.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 38 , Issue 3 , December 1988 , pp. 351 - 356
- Copyright
- Copyright © Australian Mathematical Society 1988
References
- 3
- Cited by