Liouville’s Theorem on Integration in Terms of Elementary Functions
نویسنده
چکیده
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.
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