Constrained orthogonal polynomials

Constrained Ultraspherical-Weighted Orthogonal Polynomials on Triangle

We construct Ultraspherical-weighted orthogonal polynomials C (λ,γ) n,r (u, v, w), λ > − 2 , γ > −1, on the triangular domain T, where 2λ + γ = 1. We show C (λ,γ) n,r (u, v, w), r = 0, 1, . . . , n; n ≥ 0 form an orthogonal system over the triangular domain T with respect to the Ultraspherical weight function. Mathematics Subject Classification: 33C45, 42C05, 33C70

Orthogonal Polynomials

The theory of orthogonal polynomials plays an important role in many branches of mathematics, such as approximation theory (best approximation, interpolation, quadrature), special functions, continued fractions, differential and integral equations. The notion of orthogonality originated from the theory of continued fractions, but later became an independent (and possibly more important) discipl...

Orthogonal Polynomials

Orthogonal Polynomials

In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.

Orthogonal Polynomials with Orthogonal Derivatives