Journal article
Two classes of special functions using fourier transforms of some finite classes of classical orthogonal polynomials
Publication Details
Authors:  Koepf, W.; MasjedJamei, M.

Journal:  Proceedings of the American Mathematical Society 
Abstract
Some orthogonal polynomial systems are mapped onto each other by the Fourier transform. The bestknown example of this type is the Hermite functions, i. e., the Hermite polynomials multiplied by exp(x(2)/ 2), which are eigenfunctions of the Fourier transform. In this paper, we introduce two new examples of finite systems of this type and obtain their orthogonality relations. We also estimate a complicated integral and propose a conjecture for a further example of finite orthogonal sequences.