Integration error with Chebyshev polynomials

*To*: mathgroup at smc.vnet.net*Subject*: [mg6357] Integration error with Chebyshev polynomials*From*: farmer at shire.math.columbia.edu (David Farmer)*Date*: Thu, 13 Mar 1997 01:20:14 -0500 (EST)*Organization*: Columbia University Center for Telecommunications Research*Sender*: owner-wri-mathgroup at wolfram.com

The following error was found in Mathematica 2.2: In[1]:= Integrate[E^x ChebyshevT[3,x]/Sqrt[1-x^2], {x,-1,1}] Out[1]= 0 That answer is not correct. I don't believe it can be evaluated explicitly. In any case, the answer is not 0. Mma 2.2 can do the numerical integration correctly: In[2]:= NIntegrate[E^x ChebyshevT[3,x]/Sqrt[1-x^2], {x,-1,1}] Out[2]= 0.0696442 Oddly enough, Mathematica knows that it cannot evaluate this equivalent integral: In[3]:= Integrate[E^Cos[x] Cos[3 x],{x,0,Pi}] Cos[x] Out[3]= Integrate[E Cos[3 x], {x, 0, Pi}] I am just posting this because I understand that people in a position to correct the error read this newsgroup. Maybe it has already been fixed in version 3.0. Dave