Sign equidistribution of Legendre polynomials
Abstract
We prove sign equidistribution of Legendre polynomials: the ratio between the lengths of the regions in the interval [-1, 1] where the Legendre polynomial assumes positive versus negative values, converges to one as the degree grows. The proof method also has application to the symmetry conjecture for a basis of eigenfunctions in the sphere.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.