Visualizing Laguerre polynomials as a complete orthonormal set for the inner product space ℙ n

Abstract

This linear algebra note offers teaching and learning ideas in the treatment of the orthonormal Laguerre polynomials as vectors of the inner product space with the associated improper integral inner product in a DGS (Dynamic Geometry Software)-MATLAB facilitated learning environment. The proposed learning module demonstrates creative ways of integrating DGS-MATLAB technology into various properties of the integral inner products of Laguerre polynomials along with other notions inherent in the inner product space, such as Triangle Inequality, Pythagorean Theorem, Parallelogram Law, Orthogonality and Orthonormality, Coordinates Relative to an Orthonormal Basis, and Parseval’s Identity.