Re: a bug in Mathematica 7.0?

*To*: mathgroup at smc.vnet.net*Subject*: [mg115857] Re: a bug in Mathematica 7.0?*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Sun, 23 Jan 2011 05:34:39 -0500 (EST)

----- Original Message ----- > From: "yaqi" <yaqiwang at gmail.com> > To: mathgroup at smc.vnet.net > Sent: Saturday, January 22, 2011 2:22:13 AM > Subject: [mg115836] a bug in Mathematica 7.0? > Hello, > > I was shocked by the integration result of spherical harmonics given > by Mathematica 7.0. The notebook conducting these evaluations is > attached at the end of this post. > > Basically, I create a vector of real harmonics Y={Y_{n,k},k=- > n,n;n=0,4} and then integrate Y_{n,k}*Y_{n,k}*Omega_y over the entire > 2D sphere. The integral should be zero for Y_{2,2}*Y_{4,-4}*Omega_y > but Mathematica 7.0 gives me -55*Sqrt[21]/512. Similar for Y_{4,2} > *Y_{4,-4}*Omega_y, it should be zero but I get 99*Sqrt[7]/2048. > > So I create another vector of normal spherical harmonics by using > 'SphericalHarmonicY' and then map it to the real harmonics and do the > integral mentioned above. The only difference is that I have a change > of variable in this integral; instead of using the cosine of the polor > angle, I used the polor angle for the intergal directly. This time, > Mathematica 7.0 gives me correct results. > > The only different between the two results are the two terms I > mentioned above. I did the similar thing with Mathematica 5.0. > Everything is correct. > > So can somebody take a look on the notebook, see if I messed up some > variable usages or this is indeed a bug in Mathematica 7.0? I use > Mathematica 7.0 for my regular derivations, this really shocked me! > > I do not know how to attach a file, so I copy and paste the entire > notebook and attached below. > > Many thanks. > [...] Please send the integrand and expected result for one of the bad cases. What you have is a large matrix, and I do not know which examples are problematic, let alone what specific integrands produced them. (For example, I do now know what integrand goes with the statement "Y_{2,2}*Y_{4,-4}*Omega_y". Maybe this is inexcusable ignorance on my part. Humor me.) Can send to any or all of myself, MathGroup, or Wolfram Research Tech Support. Daniel Lichtblau Wolfram Research