Alternative Equation Formats

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MathML

\begin{array}{rcl} S_{E}^{(0)} (β, k, t) & = & \sum_{j} Y_{j} (t) {1 - \frac{k - 1}{d (t)} Δ_{j} (t)} e^{β^{'} Z_{j} (t)} \\ S_{E}^{(1)} (β, k, t) & = & \sum_{j} Y_{j} (t) {1 - \frac{k - 1}{d (t)} Δ_{j} (t)} e^{β^{'} Z_{j} (t)} Z_{j} (t) \\ {\bar{Z}}_{E} β, k, t) & = & \frac{S_{E}^{(1)} (β, k, t)}{S_{E}^{(0)} (β, k, t)} \end{array}

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} S_ E^{(0)}(\bbeta ,k, t) & =& \sum _{j} Y_{j}(t) \biggl \{ 1- \frac{k-1}{d(t)} \Delta _{j}(t) \biggr \} \mr{e}^{\bbeta '\bZ _{j}(t)} \\ S_ E^{(1)}(\bbeta ,k,t) & =& \sum _{j} Y_{j}(t) \biggl \{ 1- \frac{k-1}{d(t)} \Delta _{j}(t) \biggr \} \mr{e}^{\bbeta '\bZ _{j}(t)} \bZ _{j}(t) \\ \bar{\bZ }_ E\bbeta ,k,t) & =& \frac{ S_ E^{(1)}(\bbeta ,k,t)}{ S_ E^{(0)}(\bbeta ,k,t) } \end{eqnarray*}