Logarithmic derivative near a simple pole: $\frac{f'}{f} + \frac{1}{s - p} = O(1)$ as $s \to p$ · Prove2Me

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Logarithmic derivative near a simple pole: $\frac{f'}{f} + \frac{1}{s - p} = O(1)$ as $s \to p$ · Prove2Me