Question
Expand the function f ( x = x 2 − 1 in a series of the form 
Answer :
Word Count : 162
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The question as written is incomplete, because the basis functions (B_k(x)) are not specified. In series expansions, (B_k(x)) could be Fourier functions, Legendre polynomials, Chebyshev polynomials, etc. A standard numerical-methods interpretation of this question is: > Expand (f(x)=x^2-1) as a Legendre series > [ > f(x)=\sum_{k=0}^{\infty} A_k P_k(x), > ] > where (P_k(x)) are Legendre polynomials. I will solve it under this
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