Bôcher's theorem
In mathematics, Bôcher's theorem is either of two theorems named after the American mathematician Maxime Bôcher. == Bôcher's theorem in complex analysis == In complex analysis, the theorem states that the finite zeros of the derivative r ′ ( z ) {\displaystyle r'(z)} of a non-constant rational function r ( z ) {\displaystyle r(z)} 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 ( z ) {\displaystyle r(z)} and particles of negative mass at the poles of r ( z ) {\displaystyle r(z)} , with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance.