Alternative Equation Formats

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MathML

\begin{aligned} σ_{L}^{2} & = 4 k^{2} [N p (1 - p) + Φ (d_{L}) (1 - Φ (d_{L})) - 2 {(N p (1 - p))}^{\frac{1}{2}} ϕ (d_{L})] \\ σ_{U}^{2} & = 4 k^{2} [N p (1 - p) + Φ (d_{U}) (1 - Φ (d_{U})) - 2 {(N p (1 - p))}^{\frac{1}{2}} ϕ (d_{U})] \end{aligned}

Math Rendered as SVG

Math as LaTeX Source

\begin{align*} \sigma _ L^2 & = 4k^2 \left[Np(1-p) + \Phi (d_ L)\left( 1-\Phi (d_ L) \right) - 2 \left( Np(1-p) \right)^\frac {1}{2} \phi (d_ L) \right] \\ \sigma _ U^2 & = 4k^2 \left[Np(1-p) + \Phi (d_ U)\left( 1-\Phi (d_ U) \right) - 2 \left( Np(1-p) \right)^\frac {1}{2} \phi (d_ U) \right] \\ \end{align*}