Timeline for Is there a class of functions closed against differentiation besides elementary? [closed]
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| Nov 28, 2014 at 2:57 | comment | added | fedja | That's not a good update because you can just multiply rghthndsd's $f$ by $e^x$ and no number of differentiations will ever kill this non-elementary term. You can always solve a (system of) algebraic differential equation(s) of arbitrary complexity in non-elementary functions and your conditions imply that this is more or less the general description of it with the only interesting question being to describe all algebraic first-order differential systems that have no non-elementary solutions. That may be an interesting project per se, but I'd rather stay out of it :-) | |
| Nov 28, 2014 at 0:30 | review | Reopen votes | |||
| Nov 28, 2014 at 8:57 | |||||
| Mar 17, 2014 at 11:49 | history | closed |
Misha Ricardo Andrade Stefan Kohl♦ Andrey Rekalo Chris Godsil |
Needs details or clarity | |
| Mar 16, 2014 at 18:52 | answer | added | Christopher Creutzig | timeline score: 2 | |
| Mar 16, 2014 at 14:43 | vote | accept | Anixx | ||
| Mar 16, 2014 at 14:39 | review | Close votes | |||
| Mar 17, 2014 at 11:49 | |||||
| Mar 16, 2014 at 14:36 | answer | added | rghthndsd | timeline score: 5 | |
| Mar 16, 2014 at 14:26 | comment | added | rghthndsd | @Misha This is not my understanding. When asked, Anixx linked to the wikipedia article which states such functions can be complex. Maybe I'm confused. | |
| Mar 16, 2014 at 14:24 | comment | added | Anixx | @rghthndsd I have added the requirement that the derivatives of those functions are not elementary. | |
| Mar 16, 2014 at 14:23 | history | edited | Anixx | CC BY-SA 3.0 |
added 24 characters in body
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| Mar 16, 2014 at 14:22 | comment | added | Misha | @rghthndsd: Accoring to OP's definition, $\cos(x)$ is nonelementary (for $x$ real), that's why I asked for his/her precise definition. | |
| Mar 16, 2014 at 14:22 | comment | added | Anixx | @v you're right, I will update the condition. | |
| Mar 16, 2014 at 14:21 | comment | added | rghthndsd | @Misha: $P$ needs to consist of nonelementary functions. | |
| Mar 16, 2014 at 14:20 | comment | added | rghthndsd | If I'm understanding the question right, let $g(x)$ an elementary function such that $f(x) = \int g(x)\ dx$ is not elementary. Then $P = \{f(x)\}$ works. | |
| Mar 16, 2014 at 14:20 | comment | added | Misha | OK, if you use real functions and wiki definition, just take $P$ to consist of $\cos(x)$. | |
| Mar 16, 2014 at 14:18 | comment | added | Anixx | @Misha, en.wikipedia.org/wiki/Elementary_function The functions in P may be real or complex. | |
| Mar 16, 2014 at 14:16 | comment | added | Misha | OK, what functions do you regard as "elementary" (there is no consistent terminology here). Functions from where to where? (Real or complex.) For instance, would $P=\{erf\}$ satisfy you? Please, think through what you are really asking and update your question. | |
| Mar 16, 2014 at 14:13 | comment | added | Anixx | @Misha built from finite number of functions from P and elementary functions using arithmetic operations and composition. | |
| Mar 16, 2014 at 14:09 | comment | added | Misha | What do you mean by "expressible"? Compositions and algebraic operations? Partial inverses of the functions from your class (e.g. radicals)? | |
| Mar 16, 2014 at 14:02 | history | asked | Anixx | CC BY-SA 3.0 |