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| bio | website | |
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| location | ||
| age | ||
| visits | member for | 4 months |
| seen | Apr 8 at 15:16 | |
| stats | profile views | 89 |
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Jan 3 |
accepted | Laplacian in $\mathbb{R}^n$ expressed with Christoffel symbols |
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Jan 3 |
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Laplacian in $\mathbb{R}^n$ expressed with Christoffel symbols Oh! So then if in your first equation I replace $i$ by $l$ and also replace both $p$ and $q$ by $l$ I get the expression with the $l$ from the the defintion of $g^{ij}$ right? I can't thank you enough! XD |
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Jan 3 |
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Laplacian in $\mathbb{R}^n$ expressed with Christoffel symbols Also thank you so much for your help!! |
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Jan 3 |
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Laplacian in $\mathbb{R}^n$ expressed with Christoffel symbols So the second term I managed to set equal to<br> $-\sum \frac{\partial y}{\partial x^i} \frac{\partial y}{\partial x^i} \Gamma ^j \frac{\partial f}{\partial y^k}$<br> But over which indices do I do the summation and which y components do derive in the $\frac{\partial y}{\partial x^i}$ expressions? |
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Jan 3 |
revised |
Laplacian in $\mathbb{R}^n$ expressed with Christoffel symbols edited body |
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Jan 3 |
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Laplacian in $\mathbb{R}^n$ expressed with Christoffel symbols @WillieWong Sorry again! You're right of course XD However now I'm completely lost as I don't really understand how to apply $\widetilde{\nabla}$ to $f$ |
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Jan 3 |
revised |
Laplacian in $\mathbb{R}^n$ expressed with Christoffel symbols edited body |
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Jan 3 |
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Laplacian in $\mathbb{R}^n$ expressed with Christoffel symbols @WillieWong oh, sorry about that, forgot a pair of brackets, other than that it's what I've got in my notes. I'm afraid I still don't quite see the connection between the two expressions, especially because the right hand side seems to sum over so many different indices. |
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Jan 3 |
revised |
Laplacian in $\mathbb{R}^n$ expressed with Christoffel symbols added 2 characters in body |
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Jan 3 |
awarded | Scholar |
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Jan 3 |
awarded | Supporter |
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Jan 3 |
accepted | Fourier transform of $ \frac{\sinh(kx)}{\sinh(x)}$ |
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Jan 3 |
asked | Laplacian in $\mathbb{R}^n$ expressed with Christoffel symbols |
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Jan 3 |
comment |
Fourier transform of $ \frac{\sinh(kx)}{\sinh(x)}$ Thank you! Finally managed to write a commentated solution! |
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Jan 3 |
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Fourier transform of $ \frac{\sinh(kx)}{\sinh(x)}$ @rlgordonma Oh, right forgot that the contour should be in the lower half-plane. Is the argument that because the zeros of sinh(x) don't have a limit they're countable and that's why I can use the theorem? |
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Jan 3 |
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Fourier transform of $ \frac{\sinh(kx)}{\sinh(x)}$ @rlgordonma That's the way we learned it (as far as I know) and also on wikipedia they state: "Suppose U is a simply connected open subset of the complex plane, and a1,...,an are finitely many points of U and f is a function which is defined and holomorphic on U \ {a1,...,an}." link I took that to mean, that the theorem only applied to a finite amount of residues, have I misunderstood this? |
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Jan 3 |
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Fourier transform of $ \frac{\sinh(kx)}{\sinh(x)}$ @DavideGiraudo SORRY! really bad typo :S it is still supposed to be sinh |
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Jan 3 |
awarded | Editor |
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Jan 3 |
revised |
Fourier transform of $ \frac{\sinh(kx)}{\sinh(x)}$ added 2 characters in body |
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Jan 3 |
awarded | Student |
