Question: Prove that if p(t) = p(t) is an even polynomial, then all the odd-order coefficients c 2j+1 = 0 in its Legendre expansion (4.56) vanish.

Prove that if p(t) = p(−t) is an even polynomial, then all the odd-order coefficients c2j+1 = 0 in its Legendre expansion (4.56) vanish.


p(t) = co do(t)+c q (t) + + Cn 9n (t).

p(t) = co do(t)+c q (t) + + Cn 9n (t).

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