Re: Integral with singularities

*To*: mathgroup at smc.vnet.net*Subject*: [mg116695] Re: Integral with singularities*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Thu, 24 Feb 2011 06:22:41 -0500 (EST)

What are your values for a and b? Without those, we can't duplicate your situation. Bobby On Wed, 23 Feb 2011 04:24:46 -0600, gmarkowsky at gmail.com <gmarkowsky at gmail.com> wrote: > Hello all, > > I am doing > > NIntegrate[ > 1/Sqrt[(x^2 + y^2) ((x - 1)^2 + > y^2) ((x - a)^2 + (y - b)^2)], {x, -3, 3}, {y, -3, 3}] > > Somehow it is not working very well. This doesn't seem to be a > particularly difficult request but Mathematica is having trouble. It > keeps saying stuff like > > NIntegrate::slwcon: Numerical integration converging too slowly; suspect > one of the following: singularity, value of the integration is 0, highly > oscillatory integrand, or WorkingPrecision too small. >> > > NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy > after 18 recursive bisections in x near {x,y} = {1.,2.06474}. NIntegrate > obtained 76.80413981137505` and 101.86483781265876` for the integral and > error estimates. >> > > I guess that near 0, 1, and a+bi the integrand blows up. I have tried to > exclude small areas around those points, but I don't seem to be doing it > right. Can anyone help? > > Greg > -- DrMajorBob at yahoo.com