Suppose that (g_{alpha, n}=v_{0}(alpha)+n^{-1 / 2} v_{1}(alpha)+n^{-1} v_{2}(alpha)+oleft(n^{-1}ight)) as (n ightarrow infty) where (v_{0}(alpha), v_{1}(alpha)), and (v_{2}(alpha))

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Suppose that \(g_{\alpha, n}=v_{0}(\alpha)+n^{-1 / 2} v_{1}(\alpha)+n^{-1} v_{2}(\alpha)+o\left(n^{-1}ight)\) as \(n ightarrow \infty\) where \(v_{0}(\alpha), v_{1}(\alpha)\), and \(v_{2}(\alpha)\) are constant with respect to \(n\). Prove that \(H_{3}\left(g_{\alpha, n}ight)=H_{3}\left[v_{0}(\alpha)ight]+o(1)\) and \(H_{4}\left(g_{\alpha, n}ight)=H_{4}\left[v_{0}(\alpha)ight]+o(1)\) as \(n ightarrow \infty\).

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