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\begin{aligned} \log L (ν, Σ; u_{i, 1}, \dots, u_{i, m}) \\ = \sum_{i = 1}^{n} \log g_{ν, Σ} (t_{ν}^{- 1} (u_{i, 1}), \dots, t_{ν}^{- 1} (u_{i, m})) - \sum_{i = 1}^{n} \sum_{j = 1}^{m} \log g_{ν} (t_{ν}^{- 1} (u_{i, j})) \end{aligned}

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\begin{align*} & \log L(\nu ,\Sigma ; u_{i,1},\ldots ,u_{i,m}) \\ & = \sum _{i=1}^ n \log g_{\nu ,\Sigma }(t_\nu ^{-1} (u_{i,1}), \ldots , t_\nu ^{-1} (u_{i,m})) - \sum _{i=1}^ n\sum _{j=1}^ m \log g_\nu (t_\nu ^{-1}(u_{i,j})) \end{align*}