For 
,
![lim_(epsilon_1->0; epsilon_2->0)1/(x_1-is_1epsilon_1)1/(x_2-is_2epsilon_2)
=[PV(1/(x_1))+ipis_1delta(x_1)][PV(1/(x_2))+ipis_2delta(x_2)]
+pi^2delta(x_1)delta(x_2),](/images/equations/Poincare-BertrandTheorem/NumberedEquation1.svg) |
where 
is the delta function and 
denotes the Cauchy principal
value.
Poincaré-Bertrand Theorem
See also
Delta FunctionExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Poincaré-Bertrand Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Poincare-BertrandTheorem.html