this is for holding javascript data
S More edited untitled.tex
over 8 years ago
Commit id: 422920d2d215a76404477f4edde705b836c07101
deletions | additions
diff --git a/untitled.tex b/untitled.tex
index 93c4dcb..be6675b 100644
--- a/untitled.tex
+++ b/untitled.tex
...
I_2(\mu, \sigma) = \int_{-\mu}^{0} \frac{f'}{\sqrt{2\pi}\sigma}\exp\left(-\frac{f'^2}{2\sigma^2}\right)df' + \frac{\mu}{2} \,\,{\rm erf} \left( \frac{\mu}{\sqrt{2}\sigma} \right)
\end{equation}
\begin{equation}
I_2(\mu, \sigma) =
\int_{-\mu}^{0} \int_{\mu^2/(2\sigma^2)}^{0} \frac{\sigma dt}{\sqrt{2\pi}}\exp\left(-t\right) + \frac{\mu}{2} \,\,{\rm erf} \left( \frac{\mu}{\sqrt{2}\sigma} \right)
\end{equation}
\begin{equation}
I_2(\mu, \sigma) = \frac{\sigma}{\sqrt{2\pi}}\left[ 1 -
\exp\left(-\mu\right) \exp\left(-\frac{\mu^2}{2\sigma^2}\right) \right] + \frac{\mu}{2} \,\,{\rm erf} \left( \frac{\mu}{\sqrt{2}\sigma} \right)
\end{equation}