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))

Question:

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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