Alternative Equation Formats

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MathML

h 11 , t = c 11 + a 11 2 ϵ 1 , t 1 2 + 2 a 11 a 21 ϵ 1 , t 1 ϵ 2 , t 1 + a 21 2 ϵ 2 , t 1 2 + g 11 2 h 11 , t 1 + 2 g 11 g 21 h 12 , t 1 + g 21 2 h 22 , t 1 h 12 , t = c 12 + a 11 a 12 ϵ 1 , t 1 2 + ( a 21 a 12 + a 11 a 22 ) ϵ 1 , t 1 ϵ 2 , t 1 + a 21 a 22 ϵ 2 , t 1 2 + g 11 g 12 h 11 , t 1 + ( g 21 g 12 + g 11 g 22 ) h 12 , t 1 + g 21 g 22 h 22 , t 1 h 22 , t = c 22 + a 12 2 ϵ 1 , t 1 2 + 2 a 12 a 22 ϵ 1 , t 1 ϵ 2 , t 1 + a 22 2 ϵ 2 , t 1 2 + g 12 2 h 11 , t 1 + 2 g 12 g 22 h 12 , t 1 + g 22 2 h 22 , t 1

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} h_{11,t} & =& c_{11} + a_{11}^2\epsilon ^2_{1,t-1} + 2a_{11}a_{21}\epsilon _{1,t-1}\epsilon _{2,t-1} + a_{21}^2\epsilon ^2_{2,t-1} \\ & & + g_{11}^2 h_{11,t-1} + 2g_{11}g_{21}h_{12,t-1} + g_{21}^2h_{22,t-1} \\ h_{12,t} & =& c_{12} + a_{11}a_{12}\epsilon ^2_{1,t-1} + (a_{21}a_{12}+a_{11}a_{22}) \epsilon _{1,t-1}\epsilon _{2,t-1} + a_{21}a_{22}\epsilon ^2_{2,t-1} \\ & & + g_{11}g_{12} h_{11,t-1} + (g_{21}g_{12}+g_{11}g_{22})h_{12,t-1} + g_{21}g_{22}h_{22,t-1}\\ h_{22,t} & =& c_{22} + a_{12}^2\epsilon ^2_{1,t-1} + 2a_{12}a_{22}\epsilon _{1,t-1}\epsilon _{2,t-1} + a_{22}^2\epsilon ^2_{2,t-1} \\ & & + g_{12}^2 h_{11,t-1} + 2g_{12}g_{22}h_{12,t-1} + g_{22}^2h_{22,t-1} \\ \end{eqnarray*}