S More edited untitled.tex  over 8 years ago

Commit id: 422920d2d215a76404477f4edde705b836c07101

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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}