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.
Belinsky, Integrals of Legendre polynomials and solution of some partial differential equations, Journal of Applied Analysis, Vol
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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.