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Question: Legendre economization

Question:Legendre economization

figment 8 Maple
linear student
November 09 2008
0

Hi,

I have this taylor series expansion:

> taylor(exp(-x)*sin(x), x, 11);

Now I need to do a legendre economization. So I want to write x, x², x³ etc (from the taylor series) as linear combinations of the Legendre polynomials. My idea was to simply write something like:

>solve({aP(0,x)+bP(1,x)+cP(2,x) = x²}, {a,b,c});

This is supposed to give coefficients for the legendre expansion of x². This doesn't work because it gives solutions in terms of x, which is useless to me. Is there any way?

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The analagous in Chebyshev is to write:
x²=1/2(T0 + T2)
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I need to find the same, but in terms of legendre polynomials.

Thanks.

 
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