Timeline for On a property of complex exponentials
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Oct 28, 2022 at 19:37 | comment | added | Iosif Pinelis | @Ali : Your edited post (and what you said in comments) differs greatly from your original post. | |
| Oct 28, 2022 at 19:30 | vote | accept | Ali | ||
| Oct 28, 2022 at 19:28 | comment | added | Ali | @ChristianRemling the derivative of $\gamma$ is simply the derivative of the real part plus i times the derivative of the imaginary part | |
| Oct 28, 2022 at 19:26 | history | edited | Ali | CC BY-SA 4.0 |
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| Oct 28, 2022 at 19:26 | answer | added | Alexandre Eremenko | timeline score: 4 | |
| Oct 28, 2022 at 19:25 | history | edited | Ali | CC BY-SA 4.0 |
added 20 characters in body
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| Oct 28, 2022 at 19:22 | comment | added | Ali | The integral is just supposed to be the integral of $e^z$ over a simple closed curve with respect to its lebesgue induced measure. | |
| Oct 28, 2022 at 19:12 | comment | added | Iosif Pinelis | Perhaps, I don't understand your notations/definitions. Usually, $S^1$ denotes the unit circle. In you comment, you say that $S^1$ is "the torus". Then $S^1$ must be the one-dimensional "torus" (that is, the unit circle), in order for $\gamma$ to be a curve indeed. So, it seems that then the identity map of $S^1$ is a simple smooth closed curve (if anything is a simple smooth closed curve in your setting). | |
| Oct 28, 2022 at 19:11 | comment | added | Christian Remling | @Ali: Your notation is a bit confusing since the symbol $t$ would suggest a real parameter, but then your integration is over $S^1$. Similarly, $\gamma'(t)$ is easily interpreted for real $t$, but not for a complex $t$ when $\gamma$ is just smooth (not holomorphic). | |
| Oct 28, 2022 at 18:00 | comment | added | Ali | @IosifPinelis but this does not make sense since I am asking for $\gamma$ to be a closed contour. Here $S^1$ is the torus. | |
| Oct 28, 2022 at 17:17 | comment | added | Iosif Pinelis | What about $\gamma(z)\equiv z$? | |
| Oct 28, 2022 at 16:48 | history | asked | Ali | CC BY-SA 4.0 |