Alternative Equation Formats

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MathML

\begin{aligned} Δ T_{i}^{0} & = T_{i}^{0} - T_{i - 1}^{0} \\ Δ_{i} & = δ_{i + 1}^{0} - δ_{i}^{0} \\ Q_{i} & = lim (Δ T_{i}^{0})^{- 1} \sum_{t = T_{i - 1}^{0} + 1}^{T_{i}^{0}} E (z_{t} z_{t}^{'}) \\ Ω_{i} & = lim (Δ T_{i}^{0})^{- 1} \sum_{r = T_{i - 1}^{0} + 1}^{T_{i}^{0}} \sum_{t = T_{i - 1}^{0} + 1}^{T_{i}^{0}} E (z_{r} z_{t}^{'} u_{r} u_{t}) \\ η_{i} & = Δ_{i}^{'} Q_{i + 1} Δ_{i} / Δ_{i}^{'} Q_{i} Δ_{i} \\ ϕ_{i, 1}^{2} & = Δ_{i}^{'} Ω_{i} Δ_{i} / Δ_{i}^{'} Q_{i} Δ_{i} \\ ϕ_{i, 2}^{2} & = Δ_{i}^{'} Ω_{i + 1} Δ_{i} / Δ_{i}^{'} Q_{i + 1} Δ_{i} \end{aligned}

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Math as LaTeX Source

\begin{align*} \Delta T_ i^0 & = T_ i^0 - T_{i-1}^0 \\ \Delta _ i & = \delta _{i+1}^0 - \delta _ i^0 \\ Q_ i & = \lim {(\Delta T_ i^0)^{-1}\sum _{t=T_{i-1}^0+1}^{T_ i^0}{E(z_ tz_ t')}} \\ \Omega _ i & = \lim {(\Delta T_ i^0)^{-1}\sum _{r=T_{i-1}^0+1}^{T_ i^0}{\sum _{t=T_{i-1}^0+1}^{T_ i^0}{E(z_ rz_ t'u_ ru_ t)}}} \\ \eta _ i & = \Delta _ i'Q_{i+1}\Delta _ i / \Delta _ i'Q_ i\Delta _ i \\ \phi _{i,1}^2 & = \Delta _ i'\Omega _ i\Delta _ i / \Delta _ i'Q_ i\Delta _ i \\ \phi _{i,2}^2 & = \Delta _ i'\Omega _{i+1}\Delta _ i / \Delta _ i'Q_{i+1}\Delta _ i \end{align*}