The paper's central minimization theorem is invalid because equation (36) gives the wrong norm for the polar Legendre polynomials, and the error propagates into the claimed minimum value.
Szego, Orthogonal Polynomials, 4th ed.
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Orthogonality of polar Legendre polynomials and approximation
The paper's central minimization theorem is invalid because equation (36) gives the wrong norm for the polar Legendre polynomials, and the error propagates into the claimed minimum value.