Alternative Equation Formats

The equation on this page is available in multiple formats. Depending on your browser, some formats might not render correctly.

MathML

\begin{array}{rcl} {\hat{S}}_{n} (l (n)) & = & \sum_{τ = - n + 1}^{n - 1} \hat{w} (\frac{τ}{l (n)}) D {\hat{S}}_{n, τ} D \\ {\hat{S}}_{n, τ} & = & {\begin{cases} \sum_{t = 1 + τ}^{n} [q (y_{t}, x_{t}, θ^{#}) \otimes z_{t}] [q (y_{t - τ}, x_{t - τ}, θ^{#}) \otimes z_{t - τ}]^{'} & τ \geq 0 \\ ({\hat{S}}_{n, - τ})^{'} & τ < 0 \end{cases} \\ \hat{w} (\frac{τ}{l (n)}) & = & {\begin{cases} w (\frac{τ}{l (n)}) & l (n) > 0 \\ δ_{τ, 0} & l (n) = 0 \end{cases} \end{array}

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} \hat{{\bS }}_{n}(l(n)) & =& \sum _{{\tau } = -n + 1}^{n-1}{\hat{w} ( \frac{\tau }{l(n)} ) {\bD } \hat{{\bS }}_{n,{\tau }}} {\bD } \\ \hat{{\bS }}_{n,{\tau }} & =& \begin{cases} \sum \limits _{t=1+{\tau }}^{n}{[\Strong{q} (\Strong{y}_{t}, \Strong{x}_{t},{\btheta }^{\# }) {\otimes }\Strong{z}_{t}][\Strong{q} (\Strong{y}_{t-{\tau }}, \Strong{x}_{t-{\tau }}, {\btheta }^{\# }){\otimes }\Strong{z}_{t-{\tau }}]'} & {\tau }\ge 0 \\ (\hat{{\bS }}_{n,-{\tau }})' & {\tau }<0 \end{cases}\\ \hat{w}(\frac{\tau }{l(n)}) & =& \begin{cases} w(\frac{\tau }{l(n)}) & l(n) > 0 \\ \delta _{\tau ,0} & l(n) = 0 \end{cases} \nonumber \end{eqnarray*}