A generalization of Liouville's theorem on integration in finite terms

Utsanee Leerawat; Vichian Laohakosol

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Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2002; 39(1): 13-30

Printed January 1, 2002

A generalization of Liouville's theorem on integration in finite terms

Utsanee Leerawat and Vichian Laohakosol

Kasetsart University

Abstract

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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 ${\mathcal E}{\mathcal L}$-elementary extension of Singer, Saunders and Caviness and contains the Gamma function.

Keywords: Liouville's theorem, integration in finite terms

MSC numbers: 12H05, 12H99