Orthogonal Polynomials and Fourier Orthogonal Series on a Cone

Fourier Series of Orthogonal Polynomials

It follows from Bateman [4] page 213 after setting = 1 2 . It can also be found with slight modi cation in Bateman [5] page122. However we are not aware of any reference where explicit formulas for the Fourier coef cients for Gegenbauer, Jacobi, Laguerre and Hermite polynomials can be found. In this article we use known formulas for the connection coef cients relating an arbitrary orthogonal po...

A discretized Fourier orthogonal expansion in orthogonal polynomials on a cylinder

We study the convergence of a discretized Fourier orthogonal expansion in orthogonal polynomials on B× [−1, 1], where B is the closed unit disk in R. The discretized expansion uses a finite set of Radon projections and provides an algorithm for reconstructing three dimensional images in computed tomography. The Lebesgue constant is shown to be m (log(m + 1)), and convergence is established for ...

On a Series Representation for Carleman Orthogonal Polynomials

Let {pn(z)}n=0 be a sequence of complex polynomials (pn of degree n) that are orthonormal with respect to the area measure over the interior domain of an analytic Jordan curve. We prove that each pn of sufficiently large degree has a primitive that can be expanded in a series of functions recursively generated by a couple of integral transforms whose kernels are defined in terms of the degree n...

Orthogonal Polynomials with Orthogonal Derivatives

Relative asymptotics and Fourier series of orthogonal polynomials with a discrete Sobolev inner product

Let m be a finite positive Borel measure supported in 1⁄2 1; 1 and introduce the discrete Sobolev type inner product