Weighted argument principle on a rectangle, with poles: $\frac{1}{2\pi i}\oint g\, \frac{f'}{f} = \sum_\rho m_\rho g(\rho)

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Weighted argument principle on a rectangle, with poles: $\frac{1}{2\pi i}\oint g\, \frac{f'}{f} = \sum_\rho m_\rho g(\rho) - \sum_p m_p g(p)$ · Prove2Me