Problems with Legendre expansion

*To*: mathgroup at smc.vnet.net*Subject*: [mg24402] Problems with Legendre expansion*From*: "Kevin J. McCann" <Kevin.McCann at jhuapl.edu>*Date*: Wed, 12 Jul 2000 23:13:46 -0400 (EDT)*Organization*: Johns Hopkins University Applied Physics Lab, Laurel, MD, USA*Sender*: owner-wri-mathgroup at wolfram.com

I am doing a Legendre expansion of Sin[Pi x] and have, amongst others, the following integral Integrate[Sin[Pi*x]*LegendreP[21,x],{x,-1,1}] Mathematica just returns the input with the polynomial expanded out. Now, everything about the integral is exact. We have a 21st order polynomial times the sine, and these integrals are all exact. Why no answer? This same integral does work for the 19th and 20th Legendre functions. However, complications arise even for Integrate[Sin[Pi*x]*LegendreP[19,x],{x,-1,1}] Here I do get an exact answer with Pi's and large numbers, but when I do N[%] on it, I get an answer of -0.000299144 which is way too large. If instead I do N[%,30] on the exact, I get 10^(-14). Kevin