Poisson integral with Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg23037] Poisson integral with Mathematica
- From: "Francois GRIMAL" <grimal at marius.univ-mrs.fr>
- Date: Thu, 13 Apr 2000 02:43:24 -0400 (EDT)
- Organization: Universite de la Mediterranee Aix en Provence
- Sender: owner-wri-mathgroup at wolfram.com
Mathematica 3.0 has some problems with the Poisson integrals. If you
evaluate a cell like :
Simplify[1/(2Pi)Integrate[(1+z Exp[-I u])/(1-z Exp[-I u]),{u,0,2 Pi}]]
Mathematica give the answer -1 wich is true if |z|>1 but false if |z|<1.
Now, if you evaluate the cell :
Simplify[1/(2Pi)Integrate[(1+z Exp[-I u])/(-(1-z Exp[-I u])),{u,0,2 Pi}]]
Mathematica answers -1 again but if you evaluate :
Simplify[1/(2Pi)Integrate[-(1+z Exp[-I u])/((1-z Exp[-I u])),{u,0,2 Pi}]] it
answers 1 !
The problem persists with Mathematica 4.0
How does it work ?