Consider the functions f1, f2, f3: [1,1] R defined as follows: f(x):=x f(x):= |x| for...

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Consider the functions f1, f2, f3: [1,1] → R defined as follows: f₁(x):=x f₂(x):= |x| for x € [-1, 1] for x € [-1,1] and [0 f3(x):= X for x € [-1,0] for x € (0, 1] Write down the series representation (first few (the word few is left to your interpretation) terms) for the above three functions in terms of the Legendre polynomials using the recipe given in the Legendre expansion theorem. Among the above three functions, who has the series representation with finite number of non-zero terms? Consider the functions f1, f2, f3: [1,1] → R defined as follows: f₁(x):=x f₂(x):= |x| for x € [-1, 1] for x € [-1,1] and [0 f3(x):= X for x € [-1,0] for x € (0, 1] Write down the series representation (first few (the word few is left to your interpretation) terms) for the above three functions in terms of the Legendre polynomials using the recipe given in the Legendre expansion theorem. Among the above three functions, who has the series representation with finite number of non-zero terms?

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