Alternative Equation Formats

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MathML

\begin{array}{rcl} T_{β} (d) = & \frac{1}{n} & \sum_{j = 1}^{n} \sum_{k = 1}^{n} \exp (- \frac{β^{2}}{2} | Y_{j} - Y_{k} |^{2}) \\ - & 2 (1 + β^{2})^{- d / 2} \sum_{j = 1}^{n} \exp (- \frac{β^{2}}{2 (1 + β^{2})} | Y_{j} |^{2}) + n (1 + 2 β^{2})^{- d / 2} \end{array}

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} T_{{\beta }}(d) = & \frac{1}{n}& \sum _{j=1}^{n}{\sum _{k=1}^{n}{{\exp }(- \frac{{\beta }^{2}}{2} |Y_{j} - Y_{k}|^{2})}} \\ & -& 2(1+{\beta }^{2})^{-d/2} \sum _{j=1}^{n}{{\exp }(- \frac{{\beta }^{2}}{2(1+{\beta }^{2})} |Y_{j}|^{2})} + n(1+2{\beta }^{2})^{-d/2} \nonumber \end{eqnarray*}