Expand the following in a Fourier-Legendre series for (x in(-1,1)). a. (f(x)=x^{2}). b. (f(x)=5 x^{4}+2 x^{3}-x+3). c.

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Expand the following in a Fourier-Legendre series for \(x \in(-1,1)\).

a. \(f(x)=x^{2}\).

b. \(f(x)=5 x^{4}+2 x^{3}-x+3\).

c. \(f(x)=\left\{\begin{array}{cc}-1, & -1

d. \(f(x)=\left\{\begin{array}{cc}x, & -1

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