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Asymptotic behavior of functions, asymptotic series and related topics

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Asymptotics of $K$-functional between $\ell_1$ and $\ell_2$ for a specific sequence

\tag{4} $$ Without delving into exactly what the functional $p\mapsto \lVert p^{-\max}_{-\varepsilon}\rVert_{2/3}$ in (3) is (it is the $2/3$-norm of a vector obtained from $p$), computing its asymptotics
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