A property of the zeros of the Legendre polynomials
By applying Sturm's comparison theorem, the author proves that the zeros of the Legendre polynomials \(P_ n(x)\) satisfy the following elegant inequality: \((1-x^{(n)}_{j-1})(1-x^{(n)}_{j+1})<(1-x_ j^{(n)})^ 2,\) true for all \(j\in \{2,3,...,(n-1)\}\) and \(n\in \{3,4,...\}\).
scientific article; zbMATH DE number 4075754