Alternative Equation Formats

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MathML

\begin{aligned} l (θ^{*}, p) = & - \frac{1}{2} \log | V (θ^{*}) | - \frac{f}{2} \log {r^{'} V (θ^{*})^{- 1} r} - \frac{f}{2} (1 + \log {2 π / f}) \\ l_{R} (θ^{*}, p) = & - \frac{1}{2} \log | V (θ^{*}) | - \frac{f - k}{2} \log {r^{'} V (θ^{*})^{- 1} r} \\ - \frac{1}{2} \log | X^{'} V (θ^{*})^{- 1} X | - \frac{f - k}{2} (1 + \log {2 π / (f - k)}) \end{aligned}

Math Rendered as SVG

Math as LaTeX Source

\begin{align*} l(\btheta ^*,\mb{p}) = & -\frac12 \log |\mb{V}(\btheta ^*)| -\frac{f}{2} \log \left\{ \mb{r}'\mb{V}(\btheta ^*)^{-1}\mb{r}\right\} -\frac{f}{2}(1+\log \{ 2\pi /f\} ) \\ l_ R(\btheta ^*,\mb{p}) = & -\frac12 \log |\mb{V}(\btheta ^*)| -\frac{f-k}{2} \log \left\{ \mb{r}'\mb{V}(\btheta ^*)^{-1}\mb{r}\right\} \\ & -\frac12 \log |\mb{X}'\mb{V}(\btheta ^*)^{-1}\mb{X}| -\frac{f-k}{2}(1 + \log \{ 2\pi /(f-k)\} ) \end{align*}