A Derivation of Classical Orthogonal Polynomials using Generalized Vandermonde Determinants
Rings and Algebras
2022-01-19 v2 Mathematical Physics
Functional Analysis
math.MP
Abstract
We present a derivation of classical Hermite, Laguerre, and Jacobi orthogonal polynomials directly through the Gram-Schmidt orthogonization process. The derivation uses certain generalized Vandermonde determinants with entries defined by Gamma and Beta functions. We also provide a geometric formulation of Gram-Schmidt orthogonalization using the Hodge star operator.
Cite
@article{arxiv.2106.06408,
title = {A Derivation of Classical Orthogonal Polynomials using Generalized Vandermonde Determinants},
author = {Lijing Wang},
journal= {arXiv preprint arXiv:2106.06408},
year = {2022}
}