Is this the correct use for the Levi-Civita symbol:


The lowercase "i" looks a bit off to me: $ \mathcal{E}_ijk $

Thanks in advance.

  • 5
    $\begingroup$ On Wikipedia the use \varepsilon_{ijk} when they write, for example: In three dimensions, the Levi-Civita symbol is defined by $$\varepsilon_{ijk} = \begin{cases} +1 & \text{if } (i,j,k) \text{ is } (1,2,3), (2,3,1), \text{ or } (3,1,2), \\ -1 & \text{if } (i,j,k) \text{ is } (3,2,1), (1,3,2), \text{ or } (2,1,3), \\ \;\;\,0 & \text{if } i = j, \text{ or } j = k, \text{ or } k = i \end{cases}$$ $\endgroup$ – Martin Sleziak Sep 24 '17 at 23:46
  • $\begingroup$ Bonus tip: If you highlight the entire expression on WIkipedia and copy it into here, you basically get free MathJax. $\endgroup$ – Simply Beautiful Art Sep 24 '17 at 23:51
  • $\begingroup$ @SimplyBeautifulArt The expression is a picture in Wikipedia. How can I transform picture to MathJax? $\endgroup$ – miracle173 Sep 25 '17 at 7:21
  • $\begingroup$ @miracle173 You should be able to copy the entire thing, the math formulas on Wikipedia are not made through images but LaTeX I believe. $\endgroup$ – Simply Beautiful Art Sep 25 '17 at 14:12
  • $\begingroup$ @SimplyBeautifulArt I see now if one edits the question one can get the source code, and this is Latex. $\endgroup$ – miracle173 Sep 25 '17 at 16:18

If what you want to put in the subscript is not just one symbol you need to contain everything in braces. In your example actually only $i$ is placed correctly as a subscript, which is one reason the thing does not look as you want it to look.

You should write:$\mathcal{E}_{ijk}$ for $\mathcal{E}_{ijk}$

To highlight this note $\sum_{i=1}$ vs $\sum_i=1$ $\sum_{i=1}$ vs $\sum_i=1$

Yet, note that as pointed out by Martin the symbol $\mathcal{E}$ is not commonly used in this context, instead $\varepsilon$ $\varepsilon$ is used, which is smaller than the capital E and thus the proportions relative to the subcript $i$ are different.


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