Timeline for Change of variable formulas in discrete calculus?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Jun 30, 2023 at 9:30 | history | bounty ended | Kariuki | ||
| S Jun 30, 2023 at 9:30 | history | notice removed | Kariuki | ||
| Jun 25, 2023 at 15:21 | vote | accept | Kariuki | ||
| Jun 25, 2023 at 15:15 | vote | accept | Kariuki | ||
| Jun 25, 2023 at 15:20 | |||||
| Jun 25, 2023 at 13:46 | comment | added | Michael Engelhardt | @Kariuki - The answers now given treat the issue in much more detail, but just to respond to your query in comments, also on the left hand side, it should really be $\log (x/h)$; but then the extra constant $-\log h$ is canceled once you apply the difference operator. | |
| Jun 25, 2023 at 13:14 | answer | added | Iosif Pinelis | timeline score: 2 | |
| Jun 25, 2023 at 12:01 | comment | added | Carlo Beenakker | If you know $\Delta_1^{-1}f(rx)$ you can obtain $\Delta_h^{-1}f(rx)$ by rescaling $r\mapsto rh$ and $x\mapsto x/h$. To obtain such functional inverses of the derivative operator it is easiest to transform to Fourier space, I worked this out in the answer box. | |
| Jun 25, 2023 at 11:41 | answer | added | Carlo Beenakker | timeline score: 5 | |
| S Jun 25, 2023 at 6:55 | history | bounty started | Kariuki | ||
| S Jun 25, 2023 at 6:55 | history | notice added | Kariuki | Draw attention | |
| Jun 25, 2023 at 6:54 | comment | added | Kariuki | Also, isn't the argument in $\log x$ already necessarily dimensionless? | |
| Jun 23, 2023 at 5:52 | comment | added | Kariuki | I saw that, but couldn't see how to make it work for other examples e.g. for $\Delta_h^{-1}x^a,$ or $\Delta_h^{-1}b^x$ | |
| Jun 23, 2023 at 1:43 | comment | added | Michael Engelhardt | Dimensional analysis, as you mention, would seem to be exactly what you need. In your test, the argument of a log has to be dimensionless. Any length $x$ has to be given in units of your scale $h$ in order to be quantified in a dimensionless manner. Hence, $x \rightarrow x/h$. | |
| Jun 22, 2023 at 14:38 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Jun 22, 2023 at 10:10 | history | asked | Kariuki | CC BY-SA 4.0 |