The official answer is **C,D**, using the conventional positive normalization C_n=√((2n+1)/2), since ∫P_n²=2/(2n+1). With P_n(1)=1 and P_n(−1)=(−1)ⁿ, φ₇(1)=√(15/2) and φ₆(−1)=√(13/2). Strictly, orthonormality alone fixes only |C_n|; the printed question omits the positivity convention, so arbitrary negative signs can change C and D. Official grading and this qualification are retained.
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