Alternative Equation Formats

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MathML

\begin{array}{rcl} π_{h i} & = & \frac{\partial a (γ_{h})}{\partial γ_{h i}} = \frac{\sum_{j (i)} \prod_{j = j_{1}}^{j_{m_{h}}} \exp (γ_{h j})}{\sum \prod_{j = j_{1}}^{j_{m_{h}}} \exp (γ_{h j})} \\ π_{h} & = & (π_{h 1}, \dots, π_{h n_{h}}) \\ U_{h} & = & \frac{\partial^{2} a (γ_{h})}{\partial γ_{h}^{2}} = {\frac{\partial^{2} a (γ_{h})}{\partial γ_{h i} \partial γ_{h j}}} = {a_{i j}} \\ a_{i j} & = & \frac{\sum_{k (i, j)} \prod_{k = k_{1}}^{k_{m_{h}}} \exp (γ_{h k})}{\sum \prod_{k = k_{1}}^{k_{m_{h}}} \exp (γ_{h k})} - \frac{\partial a (γ_{h})}{\partial γ_{h i}} \frac{\partial a (γ_{h})}{\partial γ_{h j}} = π_{h i j} - π_{h i} π_{h j} \end{array}

MathML rendered with MathJax

\begin{array}{rcl} π_{h i} & = & \frac{\partial a (γ_{h})}{\partial γ_{h i}} = \frac{\sum_{j (i)} \prod_{j = j_{1}}^{j_{m_{h}}} \exp (γ_{h j})}{\sum \prod_{j = j_{1}}^{j_{m_{h}}} \exp (γ_{h j})} \\ π_{h} & = & (π_{h 1}, \dots, π_{h n_{h}}) \\ U_{h} & = & \frac{\partial^{2} a (γ_{h})}{\partial γ_{h}^{2}} = {\frac{\partial^{2} a (γ_{h})}{\partial γ_{h i} \partial γ_{h j}}} = {a_{i j}} \\ a_{i j} & = & \frac{\sum_{k (i, j)} \prod_{k = k_{1}}^{k_{m_{h}}} \exp (γ_{h k})}{\sum \prod_{k = k_{1}}^{k_{m_{h}}} \exp (γ_{h k})} - \frac{\partial a (γ_{h})}{\partial γ_{h i}} \frac{\partial a (γ_{h})}{\partial γ_{h j}} = π_{h i j} - π_{h i} π_{h j} \end{array}

Math as LaTeX Source

\begin{eqnarray*} \pi _{hi} & =& \frac{\partial a(\bgamma _ h)}{\partial \gamma _{hi}} = \frac{\sum _{{j(i)}}\prod _{j=j_1}^{j_{m_ h}}\exp (\gamma _{hj})}{\sum \prod _{j=j_1}^{j_{m_ h}}\exp (\gamma _{hj})} \\ \bpi _ h & =& (\pi _{h1},\ldots ,\pi _{hn_ h}) \\ \bU _ h & =& \frac{\partial ^2 a(\bgamma _ h)}{\partial \bgamma _ h^2} = \left\{ \frac{\partial ^2\bm {a}(\bgamma _ h)}{\partial \gamma _{hi}\partial \gamma _{hj}}\right\} = \{ a_{ij}\} \\ a_{ij} & =& \frac{\sum _{{k(i,j)}}\prod _{k=k_1}^{k_{m_ h}}\exp (\gamma _{hk})}{\sum \prod _{k=k_1}^{k_{m_ h}}\exp (\gamma _{hk})} - \frac{\partial a(\bgamma _ h)}{\partial \gamma _{hi}}\frac{\partial a(\bgamma _ h)}{\partial \gamma _{hj}} = \pi _{hij} - \pi _{hi}\pi _{hj} \end{eqnarray*}