Background [TL;DR]

In Difference between Ornstein-Uhlenbeck, Vasicek and Geometric Mean Reversion, the radicals in these two equations

$$S_{T,i}=\exp\left(\ln(S_0)e^{-\alpha T}+\left(\theta-\frac{\sigma^2}{4\alpha}\right)(1-e^{-\alpha T})+\sqrt{(1-e^{-2\alpha T})\frac{\sigma^2}{2\alpha}}\epsilon_i\right)$$ and $$\ln(X_{t})=\ln(X_{t-1})e^{-\theta \Delta t}+\left(\mu-\frac{\sigma^2}{2\alpha}\right)(1-e^{-\theta \Delta t})+\sigma\sqrt{\frac{1}{2\alpha}(1-e^{-2\theta \Delta t})}\epsilon_i$$ doesn't look good as the superscript and the square root overlaps.

MWE (min. working example)

$\sqrt{a^2}$ gives $\sqrt{a^2}$.

Technical info

  • My browser: Opera 71.0.3770.198
  • My OS: Ubuntu 20.04 LTS (upgraded from 18.04 LTS)

Raison d'être

The overlapping and/or lack of vertical space between the radical sign and the superscript/numerator make reading difficult. Imagine that we have the square root of $e$ to the power $\overline{X}$ $\sqrt{e^\overline{X}}$ $\sqrt{e^\overline{X}}$. That would create confusion in reading.


I'm sure that's a problem in the MathJax library as I can't reproduce this using pdf$\rm\LaTeX$.

pdfLaTeX vs MathJax sqrt overlapping

opera vs firefox
Opera vs Firefox: the later renders the math normally

From the comments, it seems that it's a browser-specific problem. Thanks for feedback.

  • 1
    $\begingroup$ fwiw I see no issues on my iPhone. Have you tried changing the math renderer? $\endgroup$ – Calvin Khor Jan 8 at 11:40
  • 1
    $\begingroup$ Doesn't overlap for me (though there's only little space between the square in the numerator and the vinculum, but $\sqrt{e^{\overline{X}}}$ has plenty enough). What's your browser? $\endgroup$ – Daniel Fischer Jan 8 at 11:41
  • $\begingroup$ @CalvinKhor Can you clarify what "math renderer" means? It is synonymous to "math rendering system" in the sense of MathJax's official page or "math renderer" as in math.meta.stackexchange.com/q/8881/290189? $\endgroup$ – GNUSupporter 8964民主女神 地下教會 Jan 8 at 12:27
  • $\begingroup$ No overlap for me on Chrome 87.0.4280.88 64-bit on Windows 10 with HTML-CSS. $\endgroup$ – Matt Samuel Jan 8 at 12:30
  • $\begingroup$ @DanielFischer I've edited my post in response to your question. It's Opera 71. Thanks Matt for your info. $\endgroup$ – GNUSupporter 8964民主女神 地下教會 Jan 8 at 12:41
  • $\begingroup$ @GNUSupporter8964民主女神地下教會 I meant it in the second sense. Oddly I cannot find it explicitly named in the MathJax documentation; but it appears here (ctrl+F for default renderer). To find it, rightclick on any rendered MathJax then go Math Settings > Math Renderer . $\endgroup$ – Calvin Khor Jan 8 at 13:39
  • $\begingroup$ @CalvinKhor Thanks for explaining. I tested this on my laptop. I've testing some math renderers like custom HTML and MathML, but I find the math display by the default one (HTML-CSS) much prettier than the other ones that I had tried. $\endgroup$ – GNUSupporter 8964民主女神 地下教會 Jan 8 at 13:44
  • 1
    $\begingroup$ The spacing looks OK for Math Renderer HTML-CSS in Safari 14.0.2 $\endgroup$ – GEdgar Jan 8 at 15:22

Try ^\phantom{a} to create extra vertical space: $\sqrt{e^{\overline{X}^\phantom{a}}}$ gives $\sqrt{e^{\overline{X}^\phantom{a}}}$.


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