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Integration error with Chebyshev polynomials


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



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