Question: The standard Legendre polynomials, defined in the interval [1,1] are not normalized by the scalar product, but instead by setting P n (1)=1They are given

The standard Legendre polynomials, defined in the interval [−1,1] are not normalized by the scalar product, but instead by setting P n (1)=1They are given by Rodriguez' formula

Pn(x) = 1 d 2 m! dxn(x - 1). Po(x) = 1,

n≥1 i) By using this formula demonstrate that the first three polynomials are:

P(x) = x, P(x) = (3x-1).

Pn(x) = 1 d 2 m! dxn(x - 1). Po(x) = 1, P(x) = x, P(x) = (3x-1).

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