We observe that the exact connection coefficient relations transforming modal coefficients of one Jacobi Polynomial class to the modal coefficients of certain other classes are sparse. Because of this, when one of the classes corresponds to the Chebyshev case, the Fast Fourier Transform can be used to quickly compute modal coefficients for Jacobi Polynomial expansions of class (α, β) when 2α an...

We show asymptotic expansions of the eigenfunctions certain perturbations Jacobi operator in a bounded interval, deducing equiconvergence results between with respect to associated orthonormal basis and cosine basis. Several for pointwise convergence then follow.

This paper analyzes a method for solving the thirdand fifth-order differential equations with constant coefficients using a Jacobi dual-Petrov–Galerkin method, which is more reasonable than the standard Galerkin one. The spatial approximation is based on Jacobi polynomials P (α,β) n with α, β ∈ (−1, ∞) and n is the polynomial degree. By choosing appropriate base functions, the resulting system ...

We give explicitly the recurrence coefficients of a nonsymmetric semi-classical sequence of polynomials of class s = 1. This sequence generalizes the Jacobi polynomial sequence, that is, we give a new orthogonal sequence { P̂ (α,α+1) n (x,μ) } , where μ is an arbitrary parameter with (1−μ) > 0 in such a way that for μ = 0 one has the well-known Jacobi polynomial sequence { P̂ (α,α+1) n (x) } , n≥ 0.

We obtain a characterization of local Besov spaces of functions on [−1, 1] in terms of algebraic polynomial operators. These operators are constructed using the coefficients in the orthogonal polynomial expansions of the functions involved. The example of Jacobi polynomials is studied in further detail. A by-product of our proofs is an apparently simple proof of the fact that the Cesàro means o...

Abstract — In this paper we derive the matrix of transformation of the Jacobi polynomial basis form into the Bernstein polynomial basis of the same degree n and vice versa. This enables us to combine the superior least-squares performance of the Jacobi polynomials with the geometrical insight of the Bernstein form. Application to the inversion of the Bézier curves is given. 2000 Mathematics Sub...