Equiconvergence for perturbed Jacobi polynomial expansions

An Equiconvergence Theorem for a Class of Eigenfunction Expansions(') By

A recent result of Muckenhoupt concerning the convergence of the expansion of an arbitrary function in terms of the Hermite series of orthogonal polynomials is generalised to a class of orthogonal expansions which arise from an eigenfunction problem associated with a second-order linear differential equation.

Product Jacobi Expansions 3

Polynomial Expansions

The expansion of arbitrary power series in various classes of polynomial sets is considered. Some applications are also given. Notations. We will use the following contracted notation for the generalized hypergeometric function •i> •flB P q\bl,...,bQ pFAb, ^ M* z_k where p. « r(o4 k) («iOfc-n fy)*. (*v*s rw* and (°)* / = ! / = ! r(o)

The Application of the Fast Fourier Transform to Jacobi Polynomial expansions

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...

Constrained Jacobi Polynomial and Constrained Chebyshev Polynomial

In this paper, we present the constrained Jacobi polynomial which is equal to the constrained Chebyshev polynomial up to constant multiplication. For degree n = 4, 5, we find the constrained Jacobi polynomial, and for n ≥ 6, we present the normalized constrained Jacobi polynomial which is similar to the constrained Chebyshev polynomial.