Timeline for existence of antiderivatives of nasty but elementary functions
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 12, 2010 at 4:19 | comment | added | James Propp | - Jim Propp (OP) | |
| Mar 12, 2010 at 4:18 | comment | added | James Propp | Moreover, Steven Gubkin's nice example shows that Stewart's assertion that every elementary function has an elementary {\it derivative\/} (see Chapter 6 Review, True/False Question 9(a), and the answer given at the back of the book) is false unless one adds some caveats about the nature of the domain. | |
| Mar 12, 2010 at 4:07 | comment | added | Qiaochu Yuan | This answer shows that there is a second subtlety to the OP's question: it's not clear how to define integrability (from an honors calculus point of view) for a function defined on a discrete domain. | |
| Mar 12, 2010 at 0:26 | comment | added | Steven Gubkin | I thought it was clear from the initial post that the OP in functions over the reals, but it may be true that the most natural place to consider the problem is over the complex numbers. | |
| Mar 11, 2010 at 23:19 | comment | added | Jacques Carette | The theory of anti-derivatives of elementary functions is usually stated algebraically. The most natural interpretation is then over the complex rather than the reals, where the above function becomes defined everywhere (but is still extremely nasty). | |
| Mar 11, 2010 at 21:52 | history | answered | Steven Gubkin | CC BY-SA 2.5 |