Poisson's integral formula doesn't work

*To*: mathgroup at smc.vnet.net*Subject*: [mg112746] Poisson's integral formula doesn't work*From*: Sam Takoy <sam.takoy at yahoo.com>*Date*: Wed, 29 Sep 2010 04:13:20 -0400 (EDT)

Hi, Poisson's integral formula provides a solution to the Laplace equation on the unit circle with Dirichlet boundary conditions. The formula can be found here in equation (8): http://mechse.illinois.edu/research/dstn/teaching_files2/poissonformula.pdf Here's my implementation (I hope it's correct) PoissonFormula[h_] := 1/(2 Pi) Integrate[(1 - #1^2)/(1 + #1^2 - 2 #1 Cos[#2 - alpha]) h[alpha], {alpha, 0, 2 Pi}] &; $Assumptions = r > 0 && r < 1 && \[Alpha] > 0 && \[Alpha] < 2 Pi; PoissonFormula[Cos][r, \[Alpha]] The result should be r Cos[\[Alpha]] Instead, I get ((-1 + r^2) Cos[\[Alpha]])/(2 r) What's the problem here? Thanks! Sam

**Follow-Ups**:**Re: Poisson's integral formula doesn't work***From:*Mark McClure <mcmcclur@unca.edu>