Biorthogonal polynomials are constructed via LU factorization of Gram matrices, recovering Hankel-case properties, classical orthogonal polynomials, and Christoffel-Geronimus perturbation formulas.
Bochner, Über Sturm-Liouvillesche Polynomsysteme, Mathematische Zeitschrift 29 (1929) 730–736
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Revisiting Biorthogonal Polynomials. An $LU$ factorization discussion
Biorthogonal polynomials are constructed via LU factorization of Gram matrices, recovering Hankel-case properties, classical orthogonal polynomials, and Christoffel-Geronimus perturbation formulas.