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arXiv · 2106.06408

A Derivation of Classical Orthogonal Polynomials using Generalized Vandermonde Determinants

Lijing Wang
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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.

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Lijing Wang. 2021-06-11. A Derivation of Classical Orthogonal Polynomials using Generalized Vandermonde Determinants. https://arxiv.org/abs/2106.06408

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