Timeline for Taylor Series and Fourier Series [closed]
Current License: CC BY-SA 3.0
9 events
when toggle format | what | by | license | comment | |
---|---|---|---|---|---|
Jun 21, 2013 at 11:39 | history | closed |
Qiaochu Yuan Kevin Ventullo Deane Yang Andrés E. Caicedo S. Carnahan♦ |
off topic | |
Jun 20, 2013 at 6:52 | comment | added | Jochen Wengenroth | The space of formal power series is not countable dimensional: It is (isomorphic) to the space of all scalar sequences which has dimension $c$ (cardinality of the continuum). The system $\lbrace (x-a)^0, (x-a)^1,\ldots\rbrace$ is a basis for the space of all polynomials. | |
Jun 20, 2013 at 6:41 | answer | added | Alexandre Eremenko | timeline score: 2 | |
Jun 19, 2013 at 23:43 | comment | added | Noam D. Elkies | Also, a convergent Taylor (or even Laurent) series for $f(x)$ in powers of $(x-a)$ is a special case of a Fourier series (using complex exponentials in place of sines and cosines), namely for the restriction of $f$ to any circle centered at $a$ on which the series converges. | |
Jun 19, 2013 at 22:50 | comment | added | Andrés E. Caicedo | Unless you are only interested in a purely formal framework, you need to be careful with your description of these spaces. For example, not every power series is meaningful (i.e., has positive radius of convergence), and even if it is, it need not equal the function it comes from, etc. | |
Jun 19, 2013 at 22:35 | comment | added | Yemon Choi | Hmm, I am not sure (yet) that this needs to be rapidly shunted over to MSE. There is something lurking in the background about representation of differential operators on certain function spaces with respect to certain bases... although perhaps I am reading more into the question than the OP intended | |
Jun 19, 2013 at 22:14 | comment | added | paul garrett | Yes, very interesting questions, but better for Math Stack Exchange, than here. | |
Jun 19, 2013 at 21:55 | comment | added | Qiaochu Yuan | These are nice questions but not quite appropriate for MO; I'm sure they would be well-received on math.stackexchange.com. | |
Jun 19, 2013 at 21:49 | history | asked | Atif | CC BY-SA 3.0 |