A unification of Liouvillian extensions

Abstract

We generalize Liouville's theory of elementary functions to a larger class of differential extensions. Elementary, Liouvillian and trigonometric extensions are all special cases of our extensions. In the transcendental case, we show how the rational techniques of integration theory can be applied to our extensions, and we give a unified presentation which does not require separate cases for different monomials. © 1990 Springer-Verlag.