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Indeed ! But, you need to pass properly to the limit. You can use $log_s$ (the $s$ first terms of the expansion) and then remark that, when you apply both sides to a given $f\in H$, the limit is obtained by the polynomial $log_s$. log_s$ with $s$ sufficiently large.

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Indeed ! But, you need to pass properly to the limit. You can use $log_s$ (the $s$ first terms of the expansion) and then remark that, when you apply both sides to a given $f\in H$, the limit is obtained by the polynomial $log_s$.