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 | |
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| May 7, 2010 at 10:18 | comment | added | Bruce Westbury | @James The responses have been edited so we now have (more or less) a consensus on what is meant by an elementary function. I agree with Qiachou that you can define the Riemann integral of an elementary function (ignoring any caveats). My point is that there are elementary functions whose anti-derivative is not an elementary function. I took this to be a question about teaching rather than research. At a basic level "functions are defined by formulae". At this level a function is defined by a formula and you require the anti-derivative to be defined by a formula. It turns out that this fails. | |
| May 7, 2010 at 0:34 | comment | added | James Propp | Qiaochu (whose name really ought to have an "e in it somewhere, for completeness! :-) ) is correct about my intention, though I hate to say Bruce is "wrong"; most likely there was some ambiguity in my original posting. | |
| Mar 12, 2010 at 9:14 | history | edited | Bruce Westbury | CC BY-SA 2.5 |
Added response to other answers.
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| Mar 12, 2010 at 6:46 | comment | added | Bruce Westbury | That's not what OP says. The responses to this question are producing more heat than light. I have answered the question OP asked with the definition of elementary function that he had in mind. | |
| Mar 12, 2010 at 4:00 | comment | added | Qiaochu Yuan | So there are elementary functions with no elementary antiderivatives. The question is whether there exists an elementary function that is not integrable at all. | |
| Mar 11, 2010 at 20:39 | history | answered | Bruce Westbury | CC BY-SA 2.5 |