Bôcher's theorem in complex analysis 
In complex analysis, the theorem states that the finite zeros of the derivative of a nonconstant rational function 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 and particles of negative mass at the poles of , with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance.
Furthermore, if C1 and C2 are two disjoint circular regions which contain respectively all the zeros and all the poles of , then C1 and C2 also contain all the critical points of .
Bôcher's theorem for harmonic functions 
In harmonic analysis, Bôcher's theorem states that a harmonic function in punctured domain (an open domain minus one point in the interior) is a linear combination of a harmonic function in the unpunctured domain with a scaled fundamental solution for the Laplacian in that domain.
Marden's review of Walsh's book The location of critical points of analytic and harmonic functions .
|This mathematical analysis–related article is a stub. You can help Wikipedia by expanding it.|