Definitions

# Bôcher's theorem

In mathematics, Bôcher's theorem, named after Maxime Bôcher, states that the finite zeros of the derivative $r\text{'}\left(z\right)$ of a nonconstant rational function $r\left(z\right)$ that are not multiple zeros are also the positions of equilibrium in the field of force due to particles of positive mass at the zeros of $r\left(z\right)$ and particles of negative mass at the poles of $r\left(z\right)$, with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance.

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