A normal form and integration in finite terms for a class of elementary functions
Hernán Cendra · Pacific Journal of Mathematics · 1986
Let C be the field of complex numbers, E the usual exponential on C. So (C, E) is an exponential field.We define an exponential ring extension C{ JC } E of (C, E) and give a functional representation: C{x} E is isomorphic to the smallest exponential ring extension of (C, E) containing the functions ^, a? a real and positive variable, and ίeC.Finally, we give a simple integration-in-finite-terms algorithm for elements of C{x} E .