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Liouville's Theorem on Integration in Terms of Elementary Functions
| Content Provider | Semantic Scholar |
|---|---|
| Author | Churchill, R. C. |
| Copyright Year | 2003 |
| Abstract | This talk should be regarded as an elementary introduction to differential algebra. It culminates in a purely algebraic proof, due to M. Rosenlicht [Ros2], of an 1835 theorem of Liouville on the existence of “elementary” integrals of “elementary” functions. The precise meaning of elementary will be specified. As an application of that theorem we prove that the indefinite integral ∫ e 2 dx cannot be expressed in terms of elementary functions. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.sci.ccny.cuny.edu/~ksda/PostedPapers/liouv06.pdf |
| Alternate Webpage(s) | http://math.hunter.cuny.edu/ksda/papers/churchill.pdf |
| Alternate Webpage(s) | http://math.hunter.cuny.edu/ksda/papers/rick_09_02.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |