# A GENERALIZATION OF LIOUVILLE′S THEOREM ON INTEGRATION IN FINITE TERMS

• Utsanee, Leerawat (Department of Mathematics Faculty of Science Kasetsart University) ;
• Vichian, Laohakosol (Department of Mathematics Faculty of Science Kasetsart University)
• Published : 2002.01.01
• 73 10

#### Abstract

A generalization of Liouville's theorem on integration in finite terms, by enlarging the class of fields to an extension called Ei-Gamma extension is established. This extension includes the $\varepsilon$L-elementary extension of Singer, Saunders and Caviness and contains the Gamma function.

#### Keywords

Liouville′s theorem;integration in finite terms